John Utaka burst through with the interval approaching but sent a dreadful effort way off target.
Pompey continued to battle on and John Utaka hit the crossbar but the visitors, ultimately, proved too strong.
Enckelman's suspect handling was exposed when he failed to hold John Utaka's low right-wing cross and striker Kanu capitalised.
In came left-back Nadir Belhadj for his first start, and winger John Utaka was included after shaking off a knee problem.
Peter Utaka put the Danes ahead on 28 minutes to and, despite Motherwell pressure and two red cards, the visitors held on to go through.
Chasing a two-goal deficit, the visitors withdrew John Utaka for on-loan striker Milan Baros, who was denied his first Portsmouth goal when Hart made a fine stop.
Influential winger John Utaka went off injured 10 minutes later.
Hart had to be quick off his line to deny Utaka immediately after the break while James was happy to see Lee Bowyer slice a volley high and wide.
But Carlisle then went and conceded a second penalty on 75 minutes, this time hauling John Utaka down in the box, and Yebda made no mistake with a pin-point finish.
The club have made it public that Kevin-Prince Boateng and John Utaka are negotiating moves away from Fratton Park, but Cotterill could have them at his disposal for the opening games of the season.
Birmingham had Barry Ferguson to thank for clearing the ball off Utaka's head after a knock-back by the impressive Piquionne, before Seb Larsson forced James into a tip-over at the other end.
Suddenly, there was desperation in the air for Spurs and they were almost caught on the break by John Utaka, but he wasted the final pass and Luka Modric was able to recover.
O'Hara and Utaka both forced further good saves from Jensen, while at the other end Fletcher missed a glorious chance at 1-1 when, unmarked, he headed Paterson's centre over from six yards out.
The equaliser failed to dishearten Pompey and they were back in front four minutes later when Utaka cut in from the right and rifled in a shot that beat Hahnemann low to his left.
Portsmouth wasted a chance to extend their lead shortly after the break when John Utaka wriggled into space but, when he was about to shoot, team-mate Pamarot ran into his path and shot high.
Within seconds, Portsmouth swept downfield and struck the woodwork twice when Sulley Muntari's thunderous left-foot strike was pushed onto the right-hand post by Hart before Utaka smashed the resulting deflection onto the left-hand post.
Motherwell themselves have conceded just the one goal on their European travels this season, an injury-time penalty in Norway, but a real threat to that statistic will be Peter Utaka, younger brother of Portsmouth's John.
After Joel Ward replaced Utaka, Reading forward Jobi McAnuff found space but flashed a right-foot drive over the crossbar before David Nugent fluffed a chance to double Pompey's lead by miscuing his volley from 12 yards out.
Giggs, who turns 36 on Sunday, netted with a free-kick three minutes from full-time for the fourth goal and his 100th in the Premier League, while John Utaka's spectacular scissors-kick hit the crossbar with a at the other end.
Critics of Nigeria point out that the squad is ageing which led Siasia to give several players including Joel Obi, Emmanuel Emenike, Peter Utaka, and Michael Odibe their first Super Eagles starts, in a bid to revamp the squad.
The full-back latched on to John Utaka's intelligent back heel inside the box and rifled his shot into Kompany as the ball looped over Given and on to the crossbar, with Ireland clearing the danger with Danny Webber poised to pounce.
But Portsmouth reduced the deficit when Utaka's header looped over Hart on 24 minutes as City's players pleaded with the assistant referee to raise his flag for offside, only to have their requests ignored as Petrov played all of Portsmouth's attackers onside.
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