It was the hosts who had the better chances to earn a victory, but they found Hatters keeper Mark Tyler in decent form.
The result ensured that the Blues finished the year just outside of the automatic promotion places in League Two.
Paul Cook made one enforced change from the side beaten at Leyton Orient on Boxing Day.
Adam Webster served a one-match ban following his red card, so midfielder Adam Barton replaced him at centre-back.
Pompey Hall of Fame inductee Andy Awford was in the opposition dug-out and he handed a start to former Fratton loanee Paul Benson.
The hosts started brightly and Ben Davies hit a free-kick that was deflected safely into the arms of Tyler.
Marc McNulty then fired over from an acute angle after collecting a precise pass from Enda Stevens.
The Scottish striker went even closer midway through the first half, but Tyler got down quickly to push the ball clear.
Luton almost capitalised on a defensive mix-up, but Stevens came to the rescue, getting across to clear the danger.
And the left-back immediately created an opening at the other end of the pitch, with McNulty just unable to connect with a low cross as he slid in at the far post.
Kyle Bennett was next to go close when he cut across the edge of the box and struck a fierce effort that Tyler did well to keep out.
The keeper then made an even better stop moments later to prevent McNulty from breaking the deadlock.
There was a comedy moment late in the half when Davies hit a free-kick narrowly past the post.
Plenty of fans thought it had gone in and so did the announcer, who declared a goal, resulting in plenty of laughter around Fratton Park.
Luton Town 0
It was Luton who came close to scoring early in the second half, but Brian Murphy raced from his line to deny Jack Marriott before pouncing at the feet of Ryan Hall to claim the loose ball.
But the action was soon back down the other end, with Bennett surging forward and seeing his shot deflected wide.
Davies sent a corner in to the near post and Michael Doyle met it with a diving header that flew narrowly over.
The right-back delivered another dangerous corner on 58 minutes, but this time Matt Clarke’s firm header flew safely into Tyler’s arms.
Cook made his first change just past the hour mark, with Gary Roberts replacing Caolan Lavery in Pompey’s attack.
But it was Luton who were next to threaten, although Magnus Okuonghae and Craig Mackail-Smith both wasted good opportunities.
Pompey were soon back on the attack and Tyler did well to deny Evans and Roberts in quick succession, having not spotted the linesman’s raised flag.
Adam McGurk entered the fray on 77 minutes as Cook made his second switch, with McNulty the man to make way.
The chances had dried up, however, and Conor Chaplin came on for the closing stages to try to inject some life back into the Blues.
But it was Clarke who had a great chance to grab the winner in stoppage-time, only for the unmarked defender to head wide from close range.
And the Hatters held firm for the final few minutes to ensure it was honours even on Awford’s return to Fratton Park.
Pompey (4-2-3-1): Murphy; Davies, Barton, Clarke, Stevens; Hollands, Doyle (c); Evans, McNulty (McGurk 77), Bennett (Chaplin 87); Lavery (Roberts 64)
Subs not used: Bass, Close, Tollitt, Stockley
Luton (4-2-3-1): Tyler; O’Donnell, Cuthbert (c), Okuonghae, Howells; Lawless (Long 78), Smith; McQuoid (McGeehan 63), Marriott (Mackail-Smith 69), Hall; Benson
Booked: Lawless, Okuonghae, O’Donnell
Subs not used: Justham, Wilkinson, Guttridge, McCourt
Referee: Gavin Ward
Attendance: 17,668 (1,556 away fans)