Robin van Persie's penalty kick gave Manchester United a 2-1 victory over 10-man Liverpool on Sunday, settling a heated Premier League meeting between the fierce rivals after emotional tributes were paid to the Hillsborough disaster victims.
In the other big match, Laurent Koscielny spared Arsenal from a first loss of the Premier League season at Manchester City on Sunday, clinching a 1-1 draw against the defending champions.
Van Persie beat Liverpool goalkeeper Pepe Reina in the 81st minute after Antonio Valencia was fouled by Glen Johnson to secure United's first win at Anfield since December 2007.
"Over the last three or four years we've come here and played a lot better and not got anything — that's how it goes sometimes," Giggs told Sky Sports television. "It's always tough against a team like Liverpool who keep the ball well. Even if they go down to 10 men they don't change, they keep the ball, and that's always tough."
Liverpool played with 10 men for more than 50 minutes after Jonjo Shelvey's sending-off before half time but still managed to take the lead through Steven Gerrard's volley within a minute of the second half starting.
Defender Rafael da Silva equalized five minutes later, curling the ball past Reina, and Van Persie's winner ensured second-place United prolonged winless Liverpool's worst start to a season in more than 100 years.
"I thought the players were heroic in terms of performance and the spirit," Liverpool manager Brendan Rodgers said. "They were brilliant and didn't get what they deserved."
The build-up to the match, though, had been about the fallout from the report into the 1989 Hillsborough tragedy that absolved Liverpool supporters of any responsibility and exposed a police cover-up.
Old rivalries between Liverpool and United were put aside before the first match at Anfield since the report was published, with both sets of players emerging on the pitch wearing tracksuit tops featuring the number 96, the number of Reds fans crushed to death 23 years ago.
Liverpool striker Luis Suarez and United defender Patrick Evra ensured a reconciliatory start as they joined the other players in a pre-match handshake. Last season Suarez refused to shake Evra's hand when the teams played at Old Trafford after the Uruguay international was banned for racially abusing his United rival.
For the first minute of the match three sides of Anfield displayed mosaics featuring "The Truth," ''Justice" and "96."
The tributes seemed to inspire Liverpool's players on the pitch, with domination from the hosts.
Once Giggs had flashed an early shot wide the momentum was all with Liverpool as Suarez's cross-shot was stopped by Anders Lindegaard and headed away by Jonny Evans under pressure from Fabio Borini.
Gerrard drove a low effort from Shelvey's corner into the side-netting and Suarez looped a right-footed shot wide before the usuual hostilities in the north-west derby ignited.
Shelvey robbed Giggs in midfield but as the ball broke free he launched himself at Evans and the inevitable outcome was a red card.
"Jonjo Shelvey, if he gets sent off then Jonny Evans has to go as well," Rodgers said. "I think both players' feet are off the floor."
United manager Alex Ferguson was involved in a heated exchange of words as Shelvey left the pitch.
"He was trying to blame me, I suppose," Ferguson said. "Once he looks at it he can apologize if he likes."
That came after the match, with Shelvey also apologizing to the fans.
"No way was I pulling out of that tackle in a game of that importance. Im sorry," Shelvey wrote on Twitter. "I have also apologised to sir Alex, just where I come from people don't grass people up to get someone sent off."
Even with a numerical disadvantage Liverpool continued to pressure United and Suarez drew Lindegaard into a low save from his free kick.
And at the start of the second half, substitute Suso saw his cross half-cleared to Johnson. A tackle from Paul Scholes, on for Nani at half time, succeeded only in diverting the ball toward Gerrard, who volleyed home left-footed in front of the Kop.
The Reds captain, whose 10-year-old cousin Jon-Paul Gilhooley was the youngest victim at Hillsborough, whirled away pointing both arms to the sky in celebration and remembrance.
The lead was short-lived, however, and within five minutes United were level when Shinji Kagawa laid the ball off for Rafael to brilliantly curl left-footed over Reina and in off the far post.
But, even with a man down, Liverpool pushed for a winner with Suso having a shot tipped over by Lindegaard and Suarez continuing to trouble the United defense.
As the match entered the final 20 minutes United began to take more control though, and the winner came from Liverpool giving away possession on the halfway line.
Daniel Agger and Johnson collided to allow Valencia to race 50 yards into the area and, although Johnson got back, he could only bring down the Ecuador winger. Van Persie drilled home despite Reina diving the right way and getting a hand to the ball.
"We've got to be pleased with the result, but not the performance," Ferguson said.
Meanwhile, Joleon Lescott headed City in front at the end of the first half, but the defender failed to clear a corner in the 82nd minute, allowing Koscielny to score the late leveler from close range.
City's title defense has now started with two scrappy wins and three draws to sit in seventh, behind fifth-place Arsenal on goal difference.
City had been boosted by the return of Sergio Aguero for the first time since the opening weekend of the season after a knee injury, and the striker had the first real chance of the game in the 14th with a curling shot that was pushed away by goalkeeper Vito Mannone.
It was Arsenal who were looking the more dangerous, though, cutting swathes through City's midfield, and had it not been for a bad touch from Gervinho as he ran on to Aaron Ramsey's throughball, the visitors might have been ahead.
The Gunners were taking on their opponents with real pace and Carl Jenkinson did well down the right and pulled the ball back to Lukas Podolski, who could only blaze his shot well over the bar.
Gervinho then fired just wide with a shot that rippled the side-netting and drew cheers from the section of Arsenal fans down the other end who thought it had sneaked in.
The London club had not really tested goalkeeper Joe Hart, though, and they were made to pay in the 40th minute when Lescott headed in David Silva's corner.
Mannone, playing in place of the injured Wojciech Szczesny, tried to get through a ruck of defenders but got nowhere near the ball.
City could even have been two ahead at the break but Mannone partially redeemed himself with a fingertip save from Edin Dzeko's curling shot.
Arsenal continued passing the ball around neatly in the second half without really looking like scoring, and Gervinho was off target again as he blasted high and wide.
Arsenal was pressing hard but City almost decided the game on the break in the 80th when Yaya Toure played in Aguero for a shot that was smartly stopped by Mannone.
That proved crucial as Arsenal went up the other end and Santi Cazorla drew the first real save out of Hart with a fine shot from the edge of the box.
The Spaniard took the resulting corner and Lescott could only divert the ball to the feet of Koscielny, who smashed the ball into the top corner.
Arsenal had Mannone to thank for protecting the point moments later as he saved Vincent Kompany's acrobatic overhead kick before Aguero shot inches wide.