But 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 goal.
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 Luka Modric converted from the spot.
Spurs moved a point ahead of their rivals into fifth place as they inflicted a first home defeat for Dalglish, who signed a three-year contract on Thursday, since he replaced Roy Hodgson in early January.
Van der Vaart fired 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.
Anger at Webb's officiating reached a peak in the 56th minute when he penalised John Flanagan for a foul on Steven 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 Luis Suarez fired over from Flanagan's low cross while substitute Jonjo Shelvey was narrowly off target with a long-range effort.
Andy 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.
Source: PA
Source: PA