Boateng rose to connect with Richard Hughes' cross to cancel out David Bell's thunderbolt equaliser, which proved the game's one moment of rare quality.
In a poor first half, Portsmouth enjoyed the bulk of the possession but struggled to find the necessary penetration to beat Keiren Westwood.
The Coventry keeper, courted by Premier League Sunderland, denied Tommy Smith and Boateng with a fine double save inside the opening three minutes.
Westwood first kept out Smith's drive at full-stretch before diving at Boateng's feet before the Ghanaian could gobble up the rebound.
The Irish shot-stopper had to be alert again to prevent Frederic Piquionne's low cross on ten minutes landing at the feet to Boateng.
As Pompey pressed forward, Coventry remained patient and took the lead on the half hour mark through Bell.
Aron Gunnarsson played the ball cross-field to the wide man who took one touch to weigh up his options before sending an unstoppable 20-yard drive into the far corner.
Asmir Begovic did get the faintest of touches but the sheer power of the strike left the Bosnian helpless.
The upset was on but instead of keeping the momentum Coventry sat back and allowed Pompey onto them as Westwood was called on again to deny Boateng at his near post and then Piquionne.
There was only so much the Sky Blues keeper could withstand as Pompey drew level with Hughes' forward run allowing the Scottish midfielder to pick out Boateng in space and the former Spurs midfielder planted a header past Westwood.
Despite his performance in the first half, Coventry boss Chris Coleman curiously substituted Westwood in what must have been for an injury.
Replacement Dimitrios Konstantopoulos did not have to wait long until he was called into action, seizing upon Herman Hreidarsson's well-struck half-volley.
As Clinton Morrison blazed a chance over the bar at the other end, it was becoming increasingly apparent neither side possessed the necessary quality to finish the tie off.
Coleman brought on leading scorer Leon Best in the hope of forcing the issue but had Konstantopoulos to thank again as a flowing Portsmouth move involving sub Danny Webber, Younes Kaboul and finally Boateng ended with the Greek pulling off a superb one-handed save.
With Pompey having one final fling in the closing minutes of in injury time, Konstantopoulos appeared again to thwart John Utaka and Smith as Coventry held on.