They were slow to get going and some sloppy marking allowed Andy Yiadom to give the Londoners the lead.
But Chaplin and McGurk both displayed some clinical finishing either side of the break to turn the game on its head.
And the visitors’ misery was compounded when keeper Jamie Stephens was dismissed for two bookable offences.
Chaplin then grabbed his second of the afternoon just before the final whistle to complete an enjoyable afternoon for the Blues.
Paul Cook made two changes from the side that drew with Accrington the previous week.
Chaplin and McGurk both came in for the first league starts of the season, with Gareth Evans dropping to the bench and Jayden Stockley absent after just becoming a parent.
There were plenty of familiar faces in the Barnet camp, with former Pompey midfielder Martin Allen naming both Bondz N’Gala and John Akinde in his side.
The Bees boss provided an animated performance on the sidelines and received a ticking off from referee Darren England after gesturing for a home player to be booked.
But there was not too much happening on the pitch in a half that was full of commitment, but lacking in quality.
Matt Clarke had the first decent chance on 20 minutes, but could not guide Gary Roberts’ corner on target.
Instead it was the visitors who broke the deadlock soon after, with Yiadom left alone to calmly slot home Mauro Vilhete’s cut-back.
Christian Burgess had a chance to equalise when he met a Kyle Bennett free-kick, but Stephens stopped his header on the line and Chaplin then blazed the loose ball over.
But the Blues were level on 37 minutes after Barnet failed to deal with a Roberts set-piece that was sent into the box.
CHAPLIN did well to pick the ball up and make space to shoot before rifling home a fine finish past a helpless Stephens.
Brian Murphy then had to come charging out of his goal just before the break, narrowing the angle for marauding right-back Gavin Hoyte and forcing him to fire wide.
Cook made a switch at the break, with Adam Webster replacing Roberts as Pompey switched to a 3-5-2 formation.
And the hosts should have forged ahead on 52 minutes when McGurk sent Bennett through on goal, only for the summer signing to blaze high over the bar.
But McGURK was much more clinical when he raced onto Webster’s pass moments later and calmly finished past Stephens.
The visitors were not happy that the goal was allowed to stand, however, as Bennett – who did not touch the ball – was flagged offside.
The advantage might have been extended on 57 minutes, but Webster was unable to divert Ben Davies’ dangerous free-kick on target.
Barnet’s task was made a lot harder when they were reduced to 10 men midway through the second half.
Stephens came racing off his line to try to beat Bennett to the ball, but only succeeded in clattering into the Pompey midfielder.
Having already been booked for time-wasting before the break, England had no choice but to show him his second yellow card, followed by a red.
Akinde was sacrificed so teenage keeper Kai McKenzie-Lyle could come on, while Evans replaced Clarke for the hosts.
The academy stopper stopped his side from falling further behind on 82 minutes, though, tipping Chaplin’s header over the bar.
Substitute Matt Tubbs was then unable to find the target from an acute angle following a poor clearance from McKenzie-Lyle.
But it was CHAPLIN who added a gloss to the final score in stoppage-time, when a long Murphy ball was flicked on and he calmly slid the ball home.
Pompey (4-2-3-1): Murphy; Davies, Burgess, Clarke (Evans 68), Stevens; Atangana, Doyle (c); Roberts (Webster 46), Chaplin, Bennett; McGurk (Tubbs 80)
Goals: Chaplin 37, 90+6, McGurk 54
Booked: Chaplin, Stevens, Evans, Bennett, Davies
Subs not used: Jones, Tollitt, Hollands, Naismith
Barnet (4-4-1-1): Stephens; Hoyte, N’Gala, Dembele, Johnson; Vilhete (Muggleton 59), Yiadom, Togwell, Gambin (Gash 59); Weston (c); Akinde (McKenzie-Lyle 67)
Goals: Yiadom 25
Sent off: Stephens (two yellow cards)
Booked: Yiadom, Dembele
Subs not used: Nelson, Champion, Tomlinson, McLean
Referee: Darren England
Attendance: 16,217 (413 away fans)