Portsmouth won their fourth consecutive Premier League game courtesy of two late goals at the JJB Stadium.
Benjani scored his seventh Premier League goal of the season
Benjani Mwaruwari nipped in at the near post to volley home Sulley Muntari's low cross to put the visitors ahead.
And five minutes later Glen Johnson cut in unchallenged from the right and drove a low shot home from 18 yards.
Paul Scharner glanced the post with a diving header for Wigan in the first half while Muntari thundered a 30-yard free-kick on to the post for Pompey.
Sol Campbell recovered from his midweek exertions with England in Russia to start in a Portsmouth defence bolstered by Hermann Hreidarsson who passed a late fitness test.
But the Pompey back four were pulled out of shape inside the opening five minutes when Andreas Granqvist nodded Michael Brown's free-kick into the path of Scharner, however the Austrian could not mark his 50th start for the Latics with a goal.
The bright opening gave little indication of the dirge to follow.
Neither side had a meaningful effort until Kranjcar tried his luck from distance midway through the half but Kirkland dealt with the low drive comfortably despite the ball bouncing just in front of him.
The home side then wasted a couple of opportunities to test Pompey stopper David James.
Marcus Bent hit the side netting from an acute angle while Jason Koumas bent a free-kick well wide before the referee mercifully took the players off for half time.
The second half began to the tune of 2,000 Pompey fans, who had travelled for free on 40 coaches laid on by owner Alexandre Gaydamak, urging their team to 'play up'.
But the half-time teamtalks of Pompey boss Harry Redknapp and his Wigan counterpart Chris Hutchings appeared to have had little effect as misplaced passes continued to litter the pitch.
Wigan's Julius Aghahowa replaced the injured Antoine Sibierski five minutes into the half and was booked just six seconds later after clattering into Campbell.
And the Nigerian striker was then felled when trying to block Kranjcar's free-kick.
Portsmouth were becoming the more adventurous side and Campbell glanced a header wide while Hreidarsson somehow nodded over from six yards.
So it came as no surprise when Muntari found himself in enough space down the left to provide a wonderful near-post cross which Benjani turned in with a side-foot volley.
That left Wigan just nine minutes to find an equaliser.
But five minutes later, their fourth consecutive league defeat was confirmed when Johnson strolled down the right wing, cut inside and struck a low shot beyond the dive of Kirkland.
Wigan boss Chris Hutchings:
"If Scharner had scored that goal early on it might have been the spark we needed but it wasn't to be.
"I was obviously very disappointed to concede with 10 minutes to go. We had kept Benjani reasonably quiet up to that point and then he tucked it away.
"We tried to change it after the goal and they exploited the space on the counter-attack, but the second goal was very, very disappointing because we didn't pick Johnson up and it wasn't good enough."
Portsmouth boss Harry Redknapp:
"I said at half-time that the game was there for us to win.
"In games like that it is important we pick up points and I would not have been happy coming here and getting a point.
"We wouldn't have won these sorts of games six years ago because the players were useless, that's why I'm here and we've got stronger players now and we are a stronger outfit."
Wigan: Kirkland, Boyce, Granqvist, Bramble, Kilbane, Scharner, Brown, Landzaat, Koumas, Sibierski (Aghahowa 52), Bent
Subs Not Used: Pollitt, Hall, Olembe, Skoko
Booked: Aghahowa, Bramble
Portsmouth: James, Johnson, Campbell, Distin, Hreidarsson, Utaka, Davis (Pedro Mendes 77), Diop, Kranjcar, Muntari, Mwaruwari
Subs Not Used: Ashdown, Nugent, Taylor, Pamarot
Booked: Campbell, Davis, Muntari
Goals: Mwaruwari 81, Johnson 86
Ref: Peter Walton (Northamptonshire)