Liverpool's second league defeat of the season leaves them on 55 points, seven behind leaders Manchester United, who play Tottenham Hotspur in the League Cup final on Sunday and now have a game in hand.
Chelsea climbed above Liverpool into second place on goal difference after an injury-time header by Frank Lampard gave them a 2-1 home win over Wigan Athletic.
Aston Villa, fourth on 51, host Stoke City on Sunday and Arsenal's chance of catching them suffered another setback when they were held at home by Fulham for their fourth successive goalless Premier League draw.
Arsenal were booed off and are now just two points ahead of sixth-placed Everton, who beat West Bromwich Albion 2-0.
For once, Arsenal manager Arsene Wenger did not blame the opposition's negative approach for his team's failure to score.
"Fulham played well, it was not a 0-0 game. It could have been 2-2 but we lacked fresh legs," Wenger told Sky Sports.
Liverpool's failure to win the league for 20 years while continuing to taste success in the Champions League has been encapsulated by their performances in the last week.
On Wednesday they humbled Real Madrid in their own stadium but that triumph was sandwiched between a 1-1 home draw with Manchester City and Saturday's defeat by a Middlesbrough team who had not managed a league goal since Jan. 10.
Recent history, though, suggested Saturday's result was not so much of an upset because the five times European champions had won only once in their last nine visits to Middlesbrough.
OWN GOAL
Boro went ahead after 32 minutes when Stewart Downing's cross hit Xabi Alonso's thigh and flew in for an own goal.
The second came after 64 when Jeremie Aliadiere cut the ball back for Turkey forward Tuncay, who calmly converted.
Morocco's Nabil El Zhar missed a sitter for the visitors when he fired over from close range, while Dirk Kuyt also missed a great opportunity late on.
Both chances were created by Steven Gerrard but the midfielder, making his first start for almost a month, limped off 15 minutes from time with what appeared to be cramp.
"We knew we'd have to be at our best, we a were a threat going forward and were strong defensively as a team," said Boro manager Gareth Southgate.
"It was an important win for us, we've had four clean sheets in our last six, that's given us the confidence and now we are starting to score," he added after the victory moved his side out of the relegation zone.
John Terry's deflected first-half volley put Chelsea ahead against Wigan.
Steve Bruce's seventh-placed side have proved difficult opponents this season though and equalised through Olivier Kapo in the 82nd minute, only for Lampard to win it at the death.
Bruce was furious the referee didn't punish Lampard for a push on Mario Melchiot before he headed the winn
