A brace from Ahmet Brkovic, a Kevin Nicholls penalty, Peter Holmes and Sol Davis' efforts saw the table-toppers cruise past a woeful Robins outfit.
Brian Tinnion's men were lucky to keep the score down to five as the Hatters peppered the visitors' goal in a determined afternoon's work.
The returning Paul Underwood showed his value to Luton straight away with two dangerous crosses from the left in the first two minutes. The first saw Holmes have a header blocked, but the second saw Rowan Vine touch on to Steve Howard whose chipped effort twice bounced off the bar before dropping out for a goal-kick.
Underwood then nearly opened the scoring himself in the sixth minute after a flowing Luton move. Vine, Nicholls and Howard combined to set up Brkovic to cross from the right and Underwood rose well, but saw his header flash over from ten yards.
The pressure finally told as Hatters opened the scoring in the tenth minute. Davis chipped in for Underwood to again find space on the left and the 31-year-old cleverly delayed and pulled back for Brkovic to side-foot home his 13th goal of the season from eight yards.
Howard stretched Steve Phillips in the 19th minute when he powered a header towards the far corner from Holmes' deep free-kick, but the Robins keeper superbly tipped around the post.
Luton pushed on again in the 26th minute and after Howard ran clear down the left and crossed for Vine, the Pompey loan man was pulled down by the grounded Louis Carey as he challenged for the loose ball and Hatters were awarded a penalty that skipper Nicholls coolly converted for his tenth goal of the season.
City's first attempt of the day came after half-an-hour when Luke Wilkshire hit a hopeful 25-yard effort that was easily held by Marlon Beresford.
Instead, Hatters roared back with another dangerous cross from Underwood that was headed back across goal by Russell Perrett for Howard to nod past Phillips only for Coles to clear off the line.
But Luton were not to be denied and got a third before the break when Howard's shot from 18-yards was parried by Phillips, and Davis pounced on the rebound for only his second ever professional goal.
Hatters kept up the pressure after the break and Vine beat Clayton Fortune on the left in the 61st minute before crossing for Holmes to volley in his first of the season from close range.
Vine and Howard both went close before Luton made it five in the 79th minute. Holmes' corner was headed against the bar by Perrett, Vine's shot was blocked by Wilkshire, but Brkovic was on hand to tap home his second of the afternoon.