It did not look a likely outcome when Ivan Toney fired the hosts ahead early in the contest and they then dominated the rest of the first half.
The Latics hit the woodwork on three occasions, but Chey Dunkley’s red card turned the tide in the Blues’ favour.
And Chaplin’s header ensured that the noisy travelling faithful had plenty to cheer on the long trip home, despite Gareth Evans also being dismissed late on.
Kenny Jackett made three changes from the side that drew with Walsall the previous week.
Dion Donohue was handed a debut wide on the left, with Jamal Lowe returning from suspension to lead the line and Kyle Bennett also given a recall.
Kal Naismith dropped to the bench, while there was no place in the squad for Milan Lalkovic or the injured Drew Talbot.
Wigan immediately showed why they are the favourites for League One promotion and it took just eight minutes for them to break the deadlock.
Nick Powell threaded a pass through to Gavin Massey and he slid the ball across the face of goal for Toney to tap home from close range.
That failed to temper the hosts’ attacking intent and the only surprise at half-time was that they failed to extend their advantage.
It was a combination of Luke McGee and the woodwork that came to Pompey’s rescue to limit the damage.
The keeper made a fine save with his feet to deny Toney a second when the striker looked to convert a dangerous Massey delivery.
Reece James then teed-up Powell, whose fierce strike cannoned back off the crossbar on 22 minutes.
The Blues had created little at the other end of the pitch, with an uncharacteristic heavy touch from Brett Pitman denying him a shooting opportunity.
Wigan, by contrast, were looking dangerous with every attack and Christian Burgess did well to block Samy Morsy’s effort after the midfielder had initially given him the slip.
Pompey did provide more of a threat towards the end of the half and when Evans’ met a Donohue free-kick, his downwards header had to be scrambled clear.
A couple of corners also caused the Latics problems, but although Christian Walton flapped at one, they both ultimately came to nothing.
Paul Cook would have enjoyed seeing his new side dominate his old one, although that failed to stop Wigan’s boss berating the fourth official for some perceived poor refereeing decisions.
And he had more reason to moan when Toney, under pressure from Evans, could only turn Massey’s cross against the post.
The hosts looked like they would grab a second before the break, with Lee Evans’ strike heading for the net until a diving McGee managed to palm it behind.
Wigan Athletic 1
It had been virtually one-way traffic before the break, but the Blues came close to levelling just 56 seconds after the restart.
Brandon Haunstrup sent the ball into the box from wide on the left, only for Lowe to turn it wide from close range.
Wigan were soon back on the attack, however, and McGee was at his best once more to keep out Michael Jacobs’ fiercely-struck attempt.
The keeper then failed to hold another effort from the same player, but was quickly able to smother the loose ball.
Jackett made a double switch on 53 minutes in an attempt to spark a reversal of fortunes, with Donohue and Danny Rose withdrawn for Naismith and Ben Close.
And a Wigan player was also departing soon after – although there was nobody coming on to replace Dunkley.
The centre-back lashed out at Pitman off the ball and referee Robert Jones had no choice but to brandish a red card.
But it was the Latics who almost scored again on 69 minutes, with the post coming to Pompey’s rescue once more when an effort from substitute Terell Thomas beat McGee’s grasp.
The Blues were trying to make their numerical advantage count, but were finding it difficult to test Walton.
There was an equaliser for the large travelling support to cheer on 76 minutes, however.
Haunstrup swung in a fine cross from wide on the left and CHAPLIN – who had only just been brought on – deftly nodded it home.
It almost got even better for the visitors soon after, but Walton just about got down quick enough to palm clear Adam May’s daisy-cutter.
There were still chances at the other end, though, and Will Grigg should have done better than divert his far-post header straight into McGee’s arms.
But the Blues also had to play out the closing stages with 10 men when Evans’ foul earned him a second booking of the afternoon.
The fourth official’s display of six additional minutes spurred the home side on in their search for a winner.
But Pompey were able to see that out to secure a point and end Wigan’s 100 per cent start to the League One campaign.
Wigan (4-2-3-1): Walton; Byrne, Dunkley, Burn, James; Evans, Morsy (c); Massey (Colclough 83), Powell (Grigg 73), Jacobs; Toney (Thomas 61)
Goals: Toney 8
Sent off: Dunkley
Subs not used: Jones, Perkins, Gilbey, Hunt
Pompey (4-2-3-1): McGee; Evans, Burgess, Whatmough, Haunstrup; May, Rose (Close 53); Bennett (Chaplin 73), Pitman (c), Donohue (Naismith 53); Lowe
Goals: Chaplin 76
Sent off: Gareth Evans (two yellow cards)
Booked: Donohue, Pitman, Whatmough
Subs not used: Bass, Thompson, Davies, Kabamba
Referee: Robert Jones
Attendance: 9,685 (1,966 Pompey fans)