But they were forced to endure a nervy conclusion after a fine James Hanson strike reduced the Dons’ deficit.
Up until that point it had been a dominant afternoon for the visitors, with Naylor’s header opening his account for the club.
Evans doubled the advantage before the break and the Blues had several more chances to extend the lead further.
But Hanson pulled one back for Wimbledon and a tense finale ensued before the final whistle was blown.
Kenny Jackett made three changes from the side that were beaten by Gillingham in the last league fixture.
Dion Donohue was rewarded for his winning Checkatrade Trophy goal earlier in the week, while there were also returns for Ben Thompson in midfield and Oli Hawkins up front.
Brett Pitman and Ben Close both dropped to the bench, with Ronan Curtis absent on international duty.
There were a couple of familiar faces on the Wimbledon flanks, with former Pompey players Jake Jervis and Andy Barcham both starting.
The first half was a breathless affair, with the visitors in almost total control from first whistle until last.
AFC Wimbledon were indebted to Joe McDonnell in the opening stages, with the keeper saving Naylor’s header with his legs following a corner from Donohue.
He then raced off his line to deny Evans after the stand-in skipper had raced on to a great pass from Nathan Thompson.
It was an unseasonably warm afternoon in south-west London, but conditions proved difficult when the breeze picked up.
Craig MacGillivray was relatively untroubled, although he was called into action to keep out a deflected Tom Soares free-kick.
A rare spell of prolonged Dons pressure then ended with the stopper keeping out a low attempt from Jervis.
But it was Pompey on top and they deservedly broke the deadlock on 24 minutes – much to the delight of the lucky ballot winners packed into the away end.
Another fine corner from Donohue was met by NAYLOR, whose header deflected off Liam Trotter and managed to cross the line.
They kept pouring forward and Hawkins nodded narrowly wide from a Lee Brown cross, while Deji Oshilaja did well to dispossess the lively Jamal Lowe in the box.
But the advantage was doubled on 31 minutes, as Brown sent a low delivery across the face of goal and EVANS raced in at the far post to arrow a shot home.
The wind almost caught out MacGillivray at the other end, with Jervis’ cross catching a gust and landing on the roof of the net.
Still the Blues kept up their attacking intent, however, and a long-range effort from Naylor was just about pushed wide by McDonnell.
A vital block from Oshilaja then came to Wimbledon’s rescue after Lowe had bamboozled the back-line and picked out Hawkins.
The only down side for the visitors was a couple of bookings they collected from referee Lee Probert just before the interval.
Donohue was penalised for an alleged dive in the box, with Jack Whatmough booked for a late challenge on Joe Pigott.
AFC Wimbledon 0
Such had been Pompey’s dominance, that opposition manager Neal Ardley made all three of his substitutions at the break.
Tennai Watson, Barcham and Pigott were all hauled off, with Will Nightingale, Anthony Hartigan and Hanson replacing them.
The three newcomers were out there on their own for a while, however, with the rest of the home side taking an age to take to the pitch.
It was the Blues that were first to threaten after Soares had been booked for a swipe at Nathan Thompson.
Whatmough’s free-kick was nodded on by Hawkins for Lowe, who tried a cheeky back-heel that McDonnell got down to keep out.
The traffic was continuing to head in the same direction and a couple of corners almost led to more goals.
When the first of them was only partially cleared, a thunderbolt from Donohue flew narrowly off target.
He took the second himself and it was met by the head of Matt Clarke, with a well-placed Jervis clearing from the line.
But Wimbledon suddenly found themselves back in the game with a goal of their own just past the hour mark.
It was slightly unfortunate for the visitors, with Evans mis-cueing his clearance and Hanson capitalising with a fine finish that curled around MacGillivray’s dive and into the net.
The Dons might have had another soon after, but Jervis could only head the ball straight to the keeper after meeting Oshilaja’s cross.
A corner from Evans was nodded inches wide by Clarke, as Pompey tried to restore their grip on the contest.
Jackett made his first switch on 74 minutes, with Donohue the man to make way for Ben Close in midfield.
Wimbledon were playing with much more belief by this point, though, with Whatmough and Clarke both making blocks to deny Kwesi Appiah.
A second Blues change occurred soon after, with Hawkins being replaced by Pitman in the lone striking role.
The visitors were more content to use up time as the seconds ticked down, before the Pompey fans could finally celebrate another victory.
AFC Wimbledon (4-4-2): McDonnell; Watson (Nightingale 46), Oshilaja (c), McDonald, Purrington; Jervis, Trotter, Soares, Barcham (Hartigan 46); Appiah, Pigott (Hanson 46)
Goals: Hanson 63
Subs not used: King, Sibbick, Egan, Pinnock
Pompey (4-2-3-1): MacGillivray; N.Thompson, Whatmough, Clarke, Brown; Naylor, B.Thompson; Evans (c) (Walkes 89), Lowe, Donohue (Close 74); Hawkins (Pitman 80)
Goals: Naylor 24, Evans 31
Booked: Donohue, Whatmough
Subs not used: McGee, Burgess, Dennis, Mason
Referee: Lee Probert
Attendance: 4,569 (769 Pompey fans)