Alonso's first-half own goal gifted Boro the lead at the Riverside
Liverpool's title ambitions were dealt a major blow as Middlesbrough won for the first time in 15 league games.
Nabil El Zhar, Dirk Kuyt and Ryan Babel all tested Boro keeper Brad Jones but Xabi Alonso's own goal from Stewart Downing's corner put Boro ahead.
Tuncay swept in Jeremie Aliadiere's low cross to double the lead before Steven Gerrard was denied by Jones.
Marlon King tested Pepe Reina and also had a goal disallowed for offside late on as Boro ran out comfortable winners.
Liverpool, who have not won at The Riverside since a 2-1 victory in March 2002, made four changes to the side that won 1-0 at Real Madrid in the Champions League.
Steven Gerrard came in to make his 300th start for the Reds, but not even he could unlock a resolute Boro side that was unchanged from the one that beat West Ham in Wednesday's FA Cup replay.
The visitors enjoyed the better of the opening exchanges with El Zhar, making his first league start, testing Jones with a low shot from eight yards at his near post.
Missed chances frustrate Benitez
And Kuyt's rising shot on the turn from the penalty spot was tipped over by the Boro stopper who also smothered Babel's effort from an acute angle.
Boro rarely threatened unless they were able to smuggle the ball out to Downing on the left, who's pace proved problematic for makeshift right-back Martin Skrtel.
The winger's crosses also caused panic in the Liverpool box and O'Neil almost profited when he nipped in front of Aurelio at the back post, but Reina was down smartly to deal with his toe-poked effort.
However, the Liverpool keeper could do nothing to stop Boro from taking the lead.
Three Liverpool defenders missed Downing's in-swinging corner from the right and the ball cannoned into the net off Alonso's left knee.
It was Boro's first league goal since 10 January and Downing almost made it two moments later after blocking Skrtel's clearance and racing clear, but Reina saved well.
El Zhar wasted a fantastic chance to level immediately after the break when he lifted Gerrard's sublime pull-back over the bar from 12 yards with the goal at his mercy.
Somewhat against the run of play, Boro doubled their lead when O'Neil and Jeremie Aliadiere combined well down the right and the latter's low cross was swept home first time by Tuncay from the penalty spot.
Gerrard immediately set about reducing the deficit, bundling his way into Boro's box, but Jones was again equal to his effort and after a goalmouth scramble, Alonso's effort was deflected over.
Boro confidence is flowing - Southgate
Marlon King should have wrapped up the win after being found in acres of space by Tuncay, but he wanted more time than he had and Reina saved.
Liverpool captain Gerrard and Jamie Carragher were substituted and with their exit, so the Reds hopes of salvaging something from the game faded.
Downing provided one final perfect cross that O'Neill volleyed wide while King thought he had made it three when he tapped in from close range, only for the assistant referee to rule it out for offside.
Middlesbrough manager Gareth Southgate:
"We have shown in the our last three games with four points from two league games and an FA Cup win how we can play.
"We have had four clean sheets in six games and the confidence is flowing back through the players and the crowd carried us through at the end.
"This win should give the players an unbelievable amount of belief."
Liverpool manager Rafael Benitez:
"In the first 30 minutes we had around five chances and we did not take them.
"If before this game it was going to be difficult to win the league then it is clearly now going to be even harder.
"We have to think about Sunderland next before preparing to face Real Madrid in the Champions League."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.