The striker fired home in the first half to settle a match that became extremely stretched in stages.
The Blues had chances to make it a more comfortable finale, but were not made to pay for their profligacy.
Paul Cook made three changes from the side that beat Wycombe at the weekend.
Adam Barton was deployed as an emergency centre-back in place of the injured Matt Clarke (groin).
Marc McNulty (hamstring) made way for Smith up front, while Ben Davies dropped to the bench, with Kieron Freeman coming in at right-back.
Kyle Bennett (ankle), Conor Chaplin (groin), Ryan Fulton (thigh), Adam Webster (ankle), Jack Whatmough (back) and Conor Wilkinson (groin) were also sidelined for the visitors.
That meant teenage academy graduates Adam May and Christian Oxlade-Chamberlain were named among the substitutes.
It was a fairly even affair in the opening stages, with both sides looking to get forward, but neither managing to carve out many clear-cut openings.
The best fell to the hosts after eight minutes, but an unmarked Darius Charles guided his header straight at Paul Jones after meeting Callum Kennedy’s corner.
It was a similar story at the other end of the pitch, where Gareth Evans could only divert Freeman’s cross safely into the arms of Kelle Roos.
Gary Roberts then rightly picked up the game’s first booking for a mis-timed challenge on former Pompey winger Andy Barcham.
Team-mate Smith and Tom Elliott, however, seemed rather harshly punished when referee Andy Madley brandished yellow cards to both of them.
But SMITH – just like the large travelling support – was celebrating on 35 minutes when he broke the deadlock.
The home fans thought that Roberts had fouled Sean Rigg in the build-up, but Madley was uninterested and the midfielder fed Smith for a calm finish.
And the striker had the ball in the net again moments later, but this time an infringement was spotted and the goal ruled out.
There was not too many opportunities in a frantic end to the half, although the Pompey fans made their own entertainment by serenading Roberts.
AFC Wimbledon 0
There was a surprise at the start of the second half, when Brian Murphy emerged to take Jones’ place between the sticks.
He did well to claim a high ball after the Blues had failed to deal with Barry Fuller’s cross while, moments earlier, Barcham flashed a shot narrowly over.
The visitors had a chance at the other end after ex-Pompey skipper Paul Robinson had been booked for a challenge on Kal Naismith.
He was then picked out by Roberts at the far post, but the winger’s fierce drive was parried clear by Dons keeper Roos.
AFC Wimbledon were causing problems from set-pieces, though, and a free-kick was eventually scrambled clear before a corner was headed over by Elliott.
Another flag-kick then found Charles at the far post, but he headed the ball into the turf and it bounced over the bar.
And Barcham really should have punished his former side just past the hour mark, drilling a shot wide after bursting through on goal.
But Pompey missed a gilt-edged chance of their own on 72 minutes, when Roberts hurriedly shot over despite having time after collecting Evans’ pass.
And, with the Dons committing men forward, they soon had another decent opening, with Fuller well-placed on the line to stop Naismith scoring from point-blank range.
Then, just seconds later, Roberts charged through on goal, but with just Roos to beat, he sent his shot wide.
AFC Wimbledon tried to make their opponents pay for their missed chances, although Connor Smith only received a yellow card for trying to win a penalty.
And the Blues saw out the final few moments to secure all three points and leave the Dons still looking to confirm their spot in the play-offs.
AFC Wimbledon (4-4-2): Roos; Fuller (c), Robinson, Charles, Kennedy; Rigg (Reeves 46), Bulman, Smith, Barcham (Murphy 75); Taylor, Elliott (Azeez 68)
Booked: Elliott, Robinson, Smith
Subs not used: Shea, Sweeney, Fitzpatrick, Akinfenwa
Pompey (4-2-3-1): Jones (Murphy 46); Freeman, Burgess, Barton, Stevens; Hollands, Doyle (c); Evans, Roberts, Naismith; Smith
Goals: Smith 35
Booked: Roberts, Smith
Subs not used: Davies, Haunstrup, Close, May, Oxlade-Chamberlain, McGurk
Referee: Andy Madley
Attendance: 4,799 (911 Pompey fans)