However, referee Howard Webb could have been accused of having a helping hand in deciding the outcome with a series of questionable decisions which culminated in the award of a very favourable penalty for the visitors' second.
Rafael van der Vaart's volley had given Harry Redknapp's side an early lead only for Liverpool to wrest back control of the game until 11 minutes after the interval when Webb controversially pointed to the spot and Luka Modric converted.
Spurs moved a point ahead of their rivals into fifth place as they inflicted a first home defeat for Kenny Dalglish, who signed a three-year contract on Thursday, since he replaced Roy Hodgson in early January.
That formidable home record - 20 points from eight matches prior to this encounter - counted for little as the visitors took the early initiative on their way to their first Anfield victory in 19 games stretching back to 1986.
Injury robbed Dalglish of midfielder Raul Meireles, which meant he had to break up the recent successful partnership of Luis Suarez and Dirk Kuyt and bring in fit-again club record signing Andy Carroll.
It undoubtedly had a detrimental effect as the £35million England international lacks the mobility and energy of Kuyt in a front two and denied the Reds the high pressing game they have employed of late.
Spurs enjoyed their extra time on the ball and put it to good use in the early stages, dominating possession.
Van der Vaart fired well wide early on but the next time he did not disappoint with his ninth-minute shooting opportunity.
When Modric's right-wing corner skimmed off the head of Martin Skrtel he brought the ball under control with his first touch and with his second volleyed it over the crowd - helped by a deflection off Glen Johnson - past Jose Reina's left hand and into the far corner of the net.
In recent weeks everything had gone right for the Reds, unbeaten in five with 17 goals scored, but the opposite was true on this occasion.
Tottenham's closing down and tight marking prevented the hosts producing the flowing pass-and-move football which has returned under Dalglish.
The only stroke of fortune they enjoyed was the leniency of referee Howard Webb, who chose to only book Suarez for his petulant kick at Michael Dawson while he was on the floor having been angered by the defender's apparent dive to win a free-kick.
Having been brilliant in front of goal in the last month the knack appeared to have deserted Liverpool as Carroll slashed wildly at Maxi Rodriguez's pass and failed to connect properly while midfielder Jay Spearing bundled a shot wide with his weaker left foot.
The same should not have been expected of Carroll though, who wastefully headed over from six yards from Skrtel's cross.
Suarez was closer with a free-kick which flashed just wide on the stroke of half-time but the Reds needed a change as distinctive as Dalglish swapping his tracksuit for jacket and tie at the interval .
Van der Vaart lasted just five minutes into the second half before limping off to be replaced by Jermain Defoe.
Anger at Webb's officiating reached a peak in the 55th minute when he penalised John Flanagan for a foul on Pienaar when the offence appeared to be both outside the penalty area and in favour of the home side.
Modric struck home the spot-kick to give Tottenham a two-goal cushion they barely deserved.
Liverpool surged forward, enraged at the perceived injustice, and Suarez fired over from Flanagan's low cross while substitute Jonjo Shelvey was narrowly off target with a long-range effort.
Chasing the game Dalglish sent on David Ngog for Rodriguez, giving his side every opportunity to score with four strikers on the pitch.
Carroll's ineffectual display meant he was lucky to still be on when he managed his first shot on target in the 87th minute but Carlo Cudicini held it comfortably and the target man immediately replaced by Joe Cole.
Having missed out on the Champions League the Europa League may be of some consolation for Tottenham, if they can better Liverpool's result next week.
There has been an argument put forward that both sides would prefer to miss out on Europe's second-tier competition to concentrate on their league form next season.
Having tasted his first home defeat, and only the fourth of his second spell in charge, Dalglish is unlikely to be in agreement.