But the 2008 winners recovered from a lacklustre opening 45 minutes and were kept at bay by Sky Blues keeper Keiren Westwood before substitute Mokoena headed home with virtually the last touch of the game.
His goal set up a clash against Sunderland at the end of the month, but Coventry will feel extremely hard done by.
Pompey's success came on the same day as club officials met with their counterparts from Barclays Premier League to discuss their current financial situation, with a decision on their transfer embargo and television funds expected in the coming days.
Younes Kaboul and Steve Finnan were left out of Portsmouth's matchday squad, intensifying rumours of a move away from Fratton Park.
The duo were part of three changes made by manager Avram Grant from the initial 1-1 draw on January 2 - the last time Pompey played - while he was only able to name six of the permitted seven substitutes.
Coventry boss Chris Coleman, meanwhile, made two changes from the side that beat Barnsley 3-1 on Saturday, Clinton Morrison and Richard Wood coming in.
Despite City's recent impressive form - winning four of their last six - the tie failed to catch the imagination of the Sky Blues faithful with merely 7,097 inside the Ricoh Arena.
But those in attendance saw their side make an assured start.
There was very little inside the opening quarter to get excited about, although that was not deterring a buoyant Pompey following of just 487 who were in good voice regardless of the club's off-field problems.
But they were soon silenced in the 22nd minute as Best smashed home his 10th goal of the season.
Portsmouth's defence failed to deal with a long ball upfield and Michael McIndoe won a subsequent header on the edge of the area which fell to Best, and he turned well before rifling a superb half-volley into the top corner.
Kevin-Prince Boateng, who levelled matters for Pompey in the initial 1-1 draw, was presented with two good chances to do the same again but he was denied by Westwood on both occasions.
Those chances apart, the Sky Blues were looking comfortable and good value for their lead as half-time approached.
The game opened up at the start of the second half with both forward lines looking threatening, without seriously testing the scoreline.
But the visitors suffered a severe blow with 56 minutes on the clock when Boateng, who had looked their most likely route back into the clash, was forced off with an ankle injury to be replaced by John Utaka.
The first real chance of the second half came just after the hour mark as Best volleyed a pin-point David Bell cross over the bar following a swift counter-attack.
Utaka, who had added a much-needed threat to the Pompey attack since coming on, then curled an effort narrowly wide from the edge of the box before Papa Bouba Diop headed just off target as the visitors threatened a leveller.
Portsmouth were doing all the pressing as the second half wore on with Coventry's attacking threat almost non-existent.
Substitute Danny Webber saw his right-footed looped effort fly inches wide of Westwood's post and Utaka saw a goal disallowed for offside before Morrison wasted a gilt-edged chance to wrap things up having rounded Asmir Begovic.
But, with the fourth round beckoning, City shot themselves in the foot.
A ball was pumped high into the box which the hosts failed to deal with and Wright inadvertently headed the ball past Westwood, off the bar and over the line to set up a further 30 minutes.
And their was more agony to come for Coventry at the end of extra time as Mokoena's header knocked them out.