London: Sunderland's Jermain Defoe scores his side's second goal of the game against Liverpool. AP[/caption]
Manchester City lost ground after losing 1-0 at Liverpool on New Year's Eve, but they bounced back by winning 2-1 at home to Burnley despite the first-half dismissal of Fernandinho.
Liverpool, who were denied a fifth successive league win, were left five points adrift of Chelsea in second place, with City two points back in third place.
Klopp made just one change to his starting XI, Sturridge replacing the injured Jordan Henderson, and the England striker gave his side a 19th-minute lead at the Stadium of Light.
Dejan Lovren miscued his volley from a corner, but Sturridge reacted sharply to swivel and redirect the ball past Sunderland goalkeeper Vito Mannone with his head.
Defoe equalised six minutes later, netting his 10th league goal of the season from the penalty spot after Didier N'Dong was fouled by Ragnar Klavan.
Mane restored Liverpool's lead in the 72nd minute, tapping in from a corner, but then conceded a penalty for a needless handball, allowing Defoe to equalise for the second time with six minutes to play.
"There was no foul before the free-kick for the second penalty," Klopp added. "You need a little bit of luck, but Sunderland worked hard too and maybe they deserved it."
Compounding Liverpool's disappointment, Sturridge limped off late on and had to be helped to the tunnel at the full-time whistle.
Manchester City manager Pep Guardiola gave Kelechi Iheanacho a run-out in place of Sergio Aguero and the Nigerian squandered an early one-on-one with Burnley goalkeeper Tom Heaton at the Etihad Stadium.
Heaton then got down well to repel a low effort from Yaya Toure before Fernandinho was sent off in the 32nd minute for flying in on Johann Berg Gudmundsson with both feet off the ground.
It was the Brazil midfielder's third red card in six games and will earn him a four-game ban.
Guardiola turned to his bench at half-time, sending on Aguero and David Silva, and within 17 minutes of kick-off in the second half City were 2-0 up.
Left-back Gael Clichy broke the deadlock in the 58th minute, curling home with his weaker right foot, and four minutes later Aguero slammed home from a tight angle.
A blunder by Claudio Bravo allowed Ben Mee to reduce the arrears following a goalmouth scramble with 20 minutes remaining, but City held on to climb back into the Champions League places.
"We won against a lot of circumstances in a tough game so we're happy for that," Guardiola said in a slightly tetchy BBC interview.
Asked for his thoughts on Fernandinho, he replied: "Ask the referee."
Jose Mourinho's Manchester United go in search of a sixth straight league win at West Ham United later on Monday, which would take them to within a point of fourth-place Arsenal.
Substitute Enner Valencia, Leighton Baines and Romelu Lukaku scored in the last 17 minutes as seventh-place Everton overcame Southampton 3-0 at Goodison Park.
West Bromwich Albion remain a point below Everton in eighth after coming from behind to win 3-1 at home to second-bottom Hull City.
Robert Snodgrass volleyed Hull ahead, but despite losing Jonny Evans to injury, West Brom stormed back to win through goals from Chris Brunt, Gareth McAuley and James Morrison.
Champions Leicester City have now gone 12 league games without an away win following a drab 0-0 draw at Middlesbrough that left them six points above the relegation zone in 14th place.
Updated Date: Jan 02, 2017 23:14 PM