The Norwegian saw the ball deflect in off his elbow after Dave Edwards' volley from Drew Talbot's cross.
It was no more than the hard-working Hatters deserved after falling behind against the run of play to Peter Crouch's opener three minutes earlier.
The result saw cash-strapped Luton gain a much-needed pay day with a trip to Anfield, while the draw heaped more pressure on under-fire Reds boss Rafa Benitez.
The visitors took just 24 seconds to create the game's first opening as Ryan Babel beat two players on the left wing and cut inside before drawing a save off Dean Brill with a low 20-yard effort.
The hosts settled though and came tantalizingly close to taking a shock lead in the fifth minute.
David Bell superbly picked out the forward run of Edwards, but the Welsh international, with just Charles Itandje to beat, saw his shot well blocked by the Frenchmen. Then from the follow-up, Calvin Andrew blazed over.
That chance was enough to lift the volume from the home supporters, but they were almost silenced four minutes later when Kuyt played a one-two with Crouch before blazing over from 18 yards with the goal at his mercy.
The electric pace of the tie showed no sign of relenting as Kuyt twice went close for the visitors in the space of five minutes, before Talbot outstripped Sami Hyypia in the 21st minute only to see his cross-shot blocked by the legs of Itandje.
Liverpool then came alive as Crouch twice went close in the space of 60 seconds, firstly firing straight at Brill from the edge of the area after Kuyt's flick in the 34th minute and then shooting wide moments later after Kuyt's dummy from Yossi Benayoun's pass.
Talbot caused panic in the visiting defence again on the stroke of half-time as he fired in a dangerous cross from the left that just eluded Andrew at the far post.
If the visitors had been quiet at the end of the first period, they made up for it at the start of the second with two chances in the opening six minutes.
Firstly Xabi Alonso turned Edwards and Matthew Spring and found Kuyt, whose cross-shot was somehow touched past the post by Benayoun from a yard out in the 48th minute.
Three minutes later, Benayoun teed up Riise for a 25-yard thunderbolt which Brill kept out with his arm.
Luton weren't done, however, and Talbot headed Currie's 54th minute cross over the bar from six yards out when it looked easier to score, before turning and firing in a shot two minutes later only for Riise to hack clear off the line.
The deadlock was finally broken in the 73rd minute, but it was the visitors who scored against the run of play.
Chris Perry's poor header from a Liverpool long ball set substitute Andriy Voronin running clear through and although Brill saved the first effort, Crouch was on hand to put the ball into the empty net.
Amazingly, Luton rallied and grabbed an equaliser three minutes later. The hard-working Talbot somehow managed to put the ball over from near the left corner flag and Edwards, arriving at the near post managed to pressure Riise into forcing the ball over his own line from close range.
There was still time for Riise to drag an angled shot wide in the 80th minute and Edwards to send a rasping 20-yard volley just over the bar two minutes later.