Luton had frustrated Preston in the first half as they stopped them from playing but Paul Simpson's in-form side ran out comfortable winners in the second half.
In the first minute Simon Whaley's 20-yard right-foot shot flew wide of the right-hand post and six minutes later Danny Pugh's 20-yard left foot shot just missed the left-hand post.
David Nugent, on the right-hand side of the penalty area, had a 12-yard right-foot shot which went over the bar and, seven minutes later, Leon Barnett appeared to trip Chris Sedgwick in the penalty area but both the linesman and referee waved play on.
Luton's Rowan Vine then had a 30-yard right-foot shot which went over the bar and Sedgwick for Preston shot wide with a 20-yard right-foot effort.
On the half-hour mark a Sedgwick cross was deflected onto Nugent's chest and the ball ricocheted over the keeper and onto the crossbar but the danger was eventually cleared.
Pugh's right-wing left-footed corner was headed wide by Patrick Agyemang from just three yards out just before half-time.
Five minutes into the second half Nugent was through on goal and went to the keeper's right-hand side but was brought down by Marlon Beresford in the penalty area.
The referee sent off Beresford and awarded a penalty to Preston. Substitute keeper Dean Brill came on for Dean Morgan and Alexander sent the keeper the wrong way with a right-foot penalty to the keeper's right-hand side.
Pugh's left-foot right-wing corner on the hour mark was volleyed right-footed into the top left-hand corner of the net by Agyemang at the near post as he registered his fifth goal of the season.
Paul McKenna had a 20-yard shot which was on target but managed to hit the referee after 70 minutes.
With four minutes to go Sedgwick's 20-yard curling shot was parried by Brill, but substitute Brett Ormerod managed to get his right foot into the path of the ball as he diverted it into the bottom right-hand corner of the net from five yards out to make it 3-0 to Preston.