London: Marcus Rashford extended Manchester United's 100 percent start to the Premier League season with a dramatic strike two minutes into stoppage time to seal a 1-0 win at Hull City on Saturday.
Leicester finally secured the first win of their title defence with a 2-1 success against Swansea City at the King Power Stadium.
Southampton rescued a dramatic 1-1 draw against Sunderland as Jay Rodriguez's 85th-minute strike crept past goalkeeper Jordan Pickford to cancel out Jermain Defoe's 80th-minute penalty at St Mary's.
Scott Dann's late leveller gave Crystal Palace a 1-1 draw against fellow strugglers Bournemouth at Selhurst Park.
Danny Rose's 72nd-minute equaliser earned Tottenham Hotspur a 1-1 draw with Liverpool at White Hart Lane.
Everton won 1-0 against Stoke City at Goodison Park after Leighton Baines' penalty was pushed onto a post by Shay Given, only for the ball to rebound off the goalkeeper's head into the net for an own goal.
Josh King had fired Bournemouth in an 11th-minute lead before Palace midfielder Yohan Cabaye missed a penalty.
Rashford's brilliance gives United stoppage time win
Teenage forward Rashford, left out of the starting line-up for each of United's opening three matches, made his case for greater involvement as he came on as a substitute to convert Wayne Rooney's low cross from close range.
Up to that point, it looked like being an evening of frustration for Jose Mourinho's team, but they leave the KCOM Stadium in second place in the table behind leaders Chelsea only on goals scored.
Zlatan Ibrahimovic went close twice in the first half for United, while Rooney was denied by a brilliant first-half block from Hull captain Curtis Davies.
Hull, themselves looking to maintain a perfect league record, spent most of the match on the defensive but did have threatening moments of their own.
Robert Snodgrass' free-kick flew just wide in the opening half, while Tom Huddlestone's shot was deflected just wide off Eric Bailly inside the final 15 minutes.
Indeed, David Meyler lifted a shot over the bar from a promising position just seconds before Rashford struck, leaving the home side wondering what might have been.
Aside from the agonising manner of the defeat, a major concern for their caretaker manager Mike Phelan, though, will be an injury to Scotland international Snodgrass, who had to come off early in the second half.
Phelan, who is hoping to sign goalkeeper David Marshall from Cardiff City, is desperately short of senior players, despite the return of defender Harry Maguire from injury.
Hull's stand-in manager is continuing to have to field players out of position, with midfielder Jake Livermore once again filling in as a centre-back, and winger Sam Clucas figuring in a holding midfield role.
The club's lack of signings has been a sore point with supporters, who have called for owners Assem and Ehab Allam to leave the club.
Ehab, writing in the match programme, indicated that a deal has been agreed to sell the club, with a Chinese consortium led by commercial property investors Dai Yongge and Dai Xiu Li believed to be taking over, having been in negotiations for several weeks.
Despite chaos off the pitch, Hull's players have shown remarkable strength in adversity on it, withstanding United's pressure until the final seconds in torrential rain in east Yorkshire.
The visitors almost took the lead in the eighth minute, when Ibrahimovic glanced a header onto the roof of the net from Anthony Martial's clever cross.
They found it difficult to create clear chances after that and Hull did cause problems at the other end.
Marouane Fellaini conceded a free-kick right on the edge of the penalty area which Snodgrass, a regular threat from set-pieces, curled just wide.
United should have gone in front eight minutes before the interval when Juan Mata raced past Andrew Robertson and crossed for Rooney six yards out, but the England captain's effort was blocked by Davies, and the visitors' appeals for handball went unheeded.
Ibrahimovic then backheeled into the side-netting just before half-time, and United's search for a goal continued with little success for much of the second period.
Paul Pogba and substitute Henrikh Mkhitaryan both had long-range efforts that missed the target, and the match looked set for a draw until Rashford's late intervention.
Chelsea take pole position
After a dismal title defence last season, Chelsea look revitalised under new manager Antonio Conte and the Italian was able to celebrate his third successive win after the most emphatic display of his brief reign.
So disappointing last term, Eden Hazard has made a vibrant start to the new campaign and the Belgium midfielder put Chelsea ahead with a superb run and clinical finish from the edge of the penalty area in the ninth minute at Stamford Bridge.
Willian was back for Chelsea after recovering from a calf injury and the Brazil winger doubled their lead in the 41st minute before Nigeria's Victor Moses came off the bench to net the hosts' third in the 89th minute.
"It was a good performance. We have started very well this season but we must know we can improve," Conte said.
"Eden Hazard must be this decisive in every game and I'm pleased because I saw it today."
Arsenal register first win
At Vicarage Road, Arsenal's first victory of the season, after losing to Liverpool and drawing with Leicester City, should silence Wenger's critics at least temporarily.
Failing to win their first two matches while struggling to make an impact in the transfer market had prompted some Arsenal fans to turn on Wenger again after many protested against him last season.
But there were no complaints as Arsenal took the lead in the ninth minute when Santi Cazorla stroked home a penalty after Nordin Amrabat elbowed Alexis Sanchez.
Chile forward Sanchez increased Arsenal's advantage five minutes before half-time with a deft touch over Watford goalkeeper Heurelho Gomes.
Mesut Ozil was making his first start of the season after being rested following Euro 2016 and Arsenal's German playmaker made up for lost time with a headed goal in first-half stoppage time.
Watford's Roberto Pereyra reduced the deficit in the 57th minute, but the Hornets remain winless.
"I believe we shot ourselves in the foot in the first game and were under huge pressure," Wenger said.
"Today we had a good solid performance but at the moment we are not completely there physically and you could see that in the second half."
Leicester win 2-1
Claudio Ranieri's side took the lead in the 32nd minute when Jamie Vardy finished off a typically efficient counter-attack from the champions and captain Wes Morgan lashed in the second in the 52nd minute.
Riyad Mahrez wasted a chance to make it three when the winger's penalty was saved by Lukasz Fabianski and there was more frustration for Leicester when goalkeeper Kasper Schmeichel came off injured.
But Leroy Fer's 80th-minute goal for Swansea came too late to rescue a point for the visitors.
Spurs draw with Liverpool
James Milner gave Liverpool a deserved lead with a penalty in the 43rd minute after Roberto Firmino went down under the slightest contact by Erik Lamela.
But a sustained spell of second-half pressure climaxed when the unmarked Rose drilled home to preserve Tottenham's unbeaten record.