But Pompey's numerical advantage told and Dindane nodded home a Jamie O'Hara cross at the death to earn a point.
The on-loan striker then raced on to a neat Jamie O'Hara pass and turned Roger Johnson before slotting home in style.
Spurs added to their 2-1 first leg lead against Slavia when Jamie O'Hara fired in a deflected shot off Martin Latka.
Pompey did manage to carve out one chance and it took an alert Jonny Evans to clear Jamie O'Hara's goal-bound effort.
Strihavka threatened again, pulling his shot just wide from a narrow angle after getting the better of Jamie O'Hara down the right.
Michael Dawson headed Spurs level two minutes after the break and substitute Jamie O'Hara volleyed in a second five minutes later as Burnley crumbled.
Aaron Lennon poked in Jamie O'Hara's cross on two minutes and Jermain Defoe and Dimitar Berbatov forced fine saves from Craig Gordon as Spurs dominated.
Earlier, Jamie O'Hara and Didier Zokora dragged shots wide for Spurs, while Emile Heskey was denied by Heurelho Gomes and Amr Zaki headed just wide.
Dindane was denied by the legs of Craig Gordon, Jamie O'Hara almost went through on goal and Diop lashed into the side-netting from an acute angle.
But despite Brian Jensen's penalty save from Jamie O'Hara, Hassan Yebda scored a second spot-kick to win it for Pompey before Ricardo Rocha's late red card.
Martin Paterson put Burnley in front, but Michael Dawson and inspirational substitute Jamie O'Hara struck early in the second half to put the holders in front.
It could have been 5-0 by half-time as the hosts, inspired by the excellent Jamie O'Hara and Michael Brown in midfield, set about building on their crushing midweek win.
Ivorian Dindane then sent a 22-yard shot just wide and also headed past the post from 10 yards when unmarked as he met an inviting cross from Jamie O'Hara.
Both made their debuts against City, but new loan signings Jamie O'Hara and Kevin Prince Boateng of Tottenham were not registered in time as Portsmouth suffered a fourth successive defeat.
Portsmouth have been busy in the transfer market since Al Fahim's takeover with Michael Brown, Jamie O'Hara and Kevin Prince Boateng amongst a host of new faces at the Hampshire club.
Their night was summed up when Jamie O'Hara's cross was nodded down by Frederic Piquionne to the unmarked Richard Hughes, but he put his header from eight yards inexplicably past the post.
It was a rare moment of levity for the travelling fans, though, with their team - undoubtedly missing the ineligible Jamie O'Hara - all too often going through the motions without the necessary application.
Jamie O'Hara almost brought Tottenham a late reward, volleying Taarabt's deep cross narrowly wide from the angle, and Dimitar Berbatov forced a neat save with a drive, but it would have been ill-deserved after an uninspired display.
The visitors took a while to get a foothold in the game and a couple of speculative efforts from Jamie O'Hara and Jermaine Jenas flew wide, but Spurs soon went in front thanks to Pavlyuchenko's first Premier League goal.
Since joining United from Fulham, Van der Sar has won three Premier League titles and the Uefa Champions League, but did not feature in Manchester United's Carling Cup final victory over Tottenham last season when understudy Ben Foster emerged as a penalty shoot-out hero by saving a Jamie O'Hara spot-kick.
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