Rovers had to settle for a point on the south coast in a goalless encounter at a muddy Fratton Park.
The first half saw David Dunn and Chris Samba both hit the woodwork, whilst at the other end Gael Givet stopped a John Utaka effort on the line.
After Anthony Vanden Borre saw red for two bookings, Rovers had the lions share of possession and chances in the second half, but some last ditch defending allied to poor finishing was Rovers' downfall as they couldn't make their man advantage count.
Sam Allardyce made just the one change from the side that had defeated Burnley six days earlier with the fit again Paul Robinson returning to the starting line-up.
In good form following their previous week's exploits, Rovers started brightly, but couldn't fashion any clear-cut openings against a patched up Portsmouth side.
Indeed it was the home side who fashioned the first effort on goal on ten minutes when John Utaka cut inside to fire low, but it was comfortable for the returning goalkeeper.
But Rovers were pressing well, Morten Gamst Pedersen, David Dunn and Steven Nzonzi giving their hosts little time on the ball, leading to errors from the home side.
But despite their supremacy, again it was Utaka who was causing the bigger threat, getting passed Phil Jones on the byline, his shot across the bows was only palmed into the path of Jamie O'Hara, and with Robinson stranded the on-loan midfielder headed goalwards only for Gael Givet to block impressively on the line. A let-off for Rovers.
Rovers went straight up the other end and were the width of a post away from taking the lead themselves. Phil Jones with a ball into the area found Olsson trying to back-heel goalwards in the ensuing melee, the ball eventually coming out to David Dunn who steered it goalwards only for it to deflect onto the foot of the post and away.
The rain continued to pour as Portsmouth looked all the more shaky at the back. On the stroke of half-time Sam Allardyce's side should have finally taken the lead their play deserved but when a Pedersen free-kick found Chris Samba unmarked in the area, his header hit the foot of the same post Dunn's had struck earlier, El-Hadji Diouf seeing his follow-up well blocked.
The second half started as poorly as the playing conditions with both sides struggling to keep any momentum, and their footing, in the mud of Fratton Park.
Rovers were handed an advantage on the hour mark when Anthony Vanden Borre picked up his second yellow card of the game after blocking an attempted pass to Olsson with his hand. Referee Steve Bennett had no option to issue the defender the red card.
Three quickfire chances followed, a Pedersen centre was just inches away from connecting with Olsson in the six yard box, then the Swede latched onto a through ball by David Dunn, but Jamie Ashdown saved at the near post with his legs. Then after good work from Diouf, Roberts turned and shot in the area, but Ashdown was down quickly to save.
Sensing victory Sam Allardyce threw on both Junior Hoilett and Niko Kalinić, but despite plenty of possession and dangerous crosses into the area, the Portsmouth defence held firm.
At the other end, the ever-impressive Phil Jones made a vital tackle as Kanu charged through on goal. The young defender once again enhancing his growing reputation with another strong display.
Rovers pressed and pressed in the latter stages, Niko Kalinić saw a header saved and Junior Hoilett scooped over. Then in added time a Pedersen corner found its way to Phil Jones, but his poked effort appeared to hit Kalinić and bounce to safety.
The final chance fell to Martin Olsson, but he couldn't make Pompey pay when he shot straight at Jamie Ashdown.
It is another point on Rovers' travels, but they'll be making the long journey North wondering quite how they didn't pick up three.
PORTSMOUTH: Ashdown, Rocha, Mokoena (c), O'Hara, Mullins, Brown, Utaka (sub Piquionne 72 mins), Vanden Borre, Hughes (sub Sowah 64 mins), Kanu, Basinas.
Subs not used: O'Brien (GK), Nlundulu, Ward, Ritchie.
ROVERS: Robinson, Salgado, Samba (c), Jones, Givet, Diouf (sub Hoilett 77 mins), Dunn, Nzonzi (sub Grella 64 mins), Pedersen, Olsson, Roberts.
Subs not used: Brown (GK), Emerton, Linganzi, Kalinić, Di Santo.
Booked: Vanden Borre, Brown (Portsmouth), Dunn (Rovers).
Off: Vanden Borre