Second half goals from Solomon Taiwo and Luke Guttridge ensured the Hatters got off to a winning start to their campaign at Kenilworth Road.
After a frustrating first half the deadlock was broken by a 63rd-minute penalty from Taiwo and with visitors Salisbury tiring, Guttridge added a second nine minutes from time with a header from close range.
John Still made two changes, with Jon Shaw and Anthony Charles replacing Jake Howells and Alex Lacey, and the Hatters came mighty close to taking the lead inside 90 seconds when Mark Cullen, running on to an intelligent pass from Guttridge, curled a low shot inches wide of the post.
Three minutes later, as the Town pressed for an early goal, Shaw wasn’t far away from a reaching Shaun Whalley’s right-wing cross.
Salisbury were offering little in attack but on 19 minutes centre-back James Clarke headed over a decent opportunity from the hosts following a left-wing corner.
Chances were at a real premium as the first half wore on and Steve McNulty – appearing after his red card on Saturday had been overturned following an appeal – volleyed narrowly over the crossbar after the visitors had failed to clear a Town corner.
The Hatters engineered an intricate move moments before the break involving Whalley, Guttridge and Dave Martin but Shaw’s header, although on target, was comfortable for City goalkeeper James Puddy.
It was Salisbury that started the brighter after the break and the Hatters defence needed to be alert on 51 minutes following a goal-mouth scramble.
Lone visiting striker Dan Fitchett raced clear three minutes later only to send a weak effort well wide of the target, before Shaw did well to crane his neck onto a Jonathan Smith cross to test Puddy on 58 minutes.
Sensing the Town needed fresh impetus, Still sent on Andre Gray on the hour in the place of Cullen and three minutes later the substitute won a penalty that Taiwo coolly converted to send Puddy the wrong way.
With their tails up, the Hatters were now playing with some freedom with that goal in the bag and on 68 minutes Whalley was within inches of finding the bottom corner after Gray had sped clear of the City defence.
There was concern for the Town with 20 minutes left when Charles limped off and was replaced by Lacey but there was no let-up in the Hatters’ pursuit of a second goal.
Shaw almost got on the end of a superb left-wing delivery from Martin on 79 minutes but two minutes later Martin created the Hatters’ second when his cross from the right was met by the head of an unmarked Guttridge inside the six yard box to put the Town two to the good.
Whalley drove another shot inches wide with Shaw unable to make a connection when any touch would have made it 3-0 before Gray thundered a shot from range that Puddy could only gather at the second attempt.
By now the Hatters were pouring forward and it was almost three on 87 minutes when a dangerous Whalley cross from the right somehow missed Gray, Shaw and Howells all haring in to the box.
Town: Tyler; Smith, Griffiths, McNulty, Charles (sub Lacey 70); Martin (sub Howells 84), Taiwo, Guttridge, Whalley; Shaw, Cullen (sub Gray 60). Subs not used: Justham, Robinson.