The Reds led twice as they looked for a fifth straight league victory, but two penalties from Jermain Defoe ensured that Sunderland picked up a vital draw that takes them to within one point of safety.
Liverpool made the brighter start to the match, but it was Sunderland who were the first to have a shot on goal when Defoe found space 25 yards from goal and drew a good low stop from Simon Mignolet.
The visitors responded with a clear chance of their own just two minutes later, but Vito Mannone produced a fine reaction save to deny Daniel Sturridge before tipping Georginio Wijnaldum's effort over the top moments later.
Both goalkeepers were kept busy in a frantic first half and Mignolet was once again called into action against his former club shortly afterwards when he pushed Jack Rodwell's first-time effort away.
Sturridge, making his first Premier League start since October, seemed determined to make an impact, but he saw a curling effort kept out by Mannone before Sebastian Larsson turned a low Adam Lallana cross inches past his own post.
The resulting corner did provide the opening goal, though, as Sturridge reacted quickest to a mis-hit effort from Dejan Lovren, lifting a header over Mannone and in from close range.
Referee Anthony Taylor had no choice but to point to the spot, and Defore duly tucked the penalty home for his 10th goal of the season, despite Mignolet guessing the right way. Defoe has now reached double figures in 10 different Premier League seasons, joining a select group of Alan Shearer, Wayne Rooney and Frank Lampard to have achieved that feat.
It should have been 11 for the season and two in as many minutes shortly afterwards when Defoe burst onto Adnan Januzaj's through-ball and found himself with only the keeper to beat. However, Mignolet got a crucial hand to the ball as Defoe tried to take it past him, while Fabio Borini could not convert the rebound.
Rodwell was the next to test the Liverpool keeper with a looping volley from range, but the visitors were soon back on the attack themselves and Mannone twice denied identical efforts from Sturridge before half time when he ducked onto his left foot before looking to pick out the bottom far corner.
The second half began at a slower tempo compared to the frenetic pace of the first as Sunderland sat deeper and challenged Liverpool to break them down.
Sunderland had a chance of their own moments later when Borini broke into the box, but the Liverpool defence blocked shots from both him and Defoe before the referee waved away penalty claims for a handball against Emre Can.
It was Liverpool who continued to look the most like scoring, though, and Mannone made two routine stops from Roberto Firmino and Can before keeping his side level with a big save to deny Sturridge after a clever one-two with Lallana had sent the Liverpool goalscorer one on one with the keeper.
However, the visitors did regain their lead from the resulting corner when Papy Djilobodji inadvertently flicked the ball into the path of Mane, who was left with a simple tap-in from close range.
Once again Sunderland were able to respond with an equaliser, though, and it came via the same route as their first goal as Defoe tucked the ball home from the penalty spot after Larsson's free kick had struck the hand of Mane inside the area.
Mannone still had work to do to keep his side level, but he successfully denied Klavan, Lallana and Firmino in the closing stages to ensure that his side came away with an important point.
The Black Cats now sit just one point from safety having lost just one of their last five home league games, with today's draw handing them their first point against a current top-seven team this season.
Liverpool, meanwhile, are now five points behind Chelsea but could see that gap grow to eight should the leaders make it 14 wins in a row against Tottenham Hotspur at White Hart Lane on Wednesday.