Marc Edworthy was sent off in the fifth minute for bringing down Pompey's Diomansy Kamara as he threatened to race onto the ball after a Simon Charlton blunder.
Ten-man City were obliged to spend the rest of the match defending, with Craig Fleming and Gary Doherty outstanding.
But ultimately it was Green who prevented Portsmouth from snatching an undeserved victory by keeping out late shots from Valery Mezague and full-back Andy Griffin.
Mazague was played clear by a shrewd pass from Yakubu but saw his shot blocked by the goalkeeper.
Then a low shot from Griffin was pushed to safety by the goalkeeper at the foot of the post.
Norwich went into the match without an away win this season but they took a shock lead in the ninth minute with a stunning goal by Damien Francis.
Darren Huckerby's right-wing cross was only half-cleared by Arjan De Zeeuw and Francis picked out the top left-hand corner of the net with a superb right-footed volley.
Yakubu should have equalised within a minute when Matt Taylor crossed from the left, but the Nigerian striker tucked a header into the side-netting.
Charlton then cleared Patrick Berger's shot off the line before Shaka Hislop saved at the feet of Leon McKenzie.
Kamara had the Norwich defence on the ropes again in the 16th minute, twisting his way past two defenders before shooting just wide from the edge of the penalty area.
Francis should have doubled his and Norwich's tally in the 23rd minute when he headed Huckerby's cross wide.
After the break Kamara fired narrowly wide with a speculative 25-yard strike while at the other end David Bentley fired wide.
Pompey equalised in the 61st minute thanks to a thrice-taken penalty from Yakubu.
McKenzie was adjudged to have handled inside the box and referee Dowd pointed to the spot.
But Dowd spotted Kamara encroaching as Yakubu twice netted before finally beating Green for a third time to make it 1-1.
MAN OF THE MATCH: Robert Green (Norwich) - Ensured the Canaries hung on for a well-deserved point with a string of fine saves.