An excellent goalkeeping performance from systems engineer Chris Hill saved part-timers Guiseley from a heavier defeat.
Hill pulled off a string of excellent saves as Joe Kinnear's men peppered the Unibond League first division side's goal with 17 shots on target.
However, Hatters' Croatian midfielder Ahmet Brkovic did manage to beat Hill twice after scoring a midweek LDV Vans Trophy hat-trick at Stevenage. Matthew Spring and Tony Thorpe were the Hatters' other scorers.
Midfielder Spring opened the scoring after just three minutes when he fired an unstoppable 30-yard drive into Hill's bottom corner.
Steve Howard then somehow contrived to head over an empty goal after Spring's free-kick had clipped the Guiseley defensive wall and hit the crossbar.
Home defender Chris Coyne blazed over in the 11th minute and Hill then charged off his line to save at Thorpe's feet.
Hill's best save of the match came in the 31st minute when he pulled off a brilliant acrobatic stop to tip over Howard's header.
Thorpe was denied by Hill again in the 42nd minute before 40-year-old defender Clive Freeman saw his 35-yard drive fly high and wide at the other end.
But Luton took control of the tie with two goals in the first half's last two minutes.
Thorpe belatedly beat Hill when he met Brkovic's cross with a close-range header at the far post.
Brkovic got his first of the afternoon when he squeezed a 15-yard shot between Hill and his near post after Howard's pass.
Guiseley's sole striker, Ryan Senior, forced Carl Emberson into a 57th minute save after a strong run into the penalty box.
But Brkovic was back on the score-sheet in the 67th minute, stabbing the ball over the line after Thorpe had headed a Spring cross towards goal.
Guiseley went close to netting a consolation in the last ten minutes.
First, Freeman curled a free-kick inches over from 20 yards and Peter Sumner then sent two flashing drives just wide of Emberson's goal