Turner (right) scored as Pompey struggled to defend set-pieces
Noe Pamarot put the ball into his own net as Hull snatched a dramatic late equaliser at Portsmouth.
Papa Bouba Diop hit the crossbar before Peter Crouch headed home Younes Kaboul's cross to put Pompey in front.
Geovanni hit the crossbar from long- range but Michael Turner did equalise with a header from a corner.
Glen Johnson put Pompey back in front with a spectacular volley but Pamarot headed into his own net under pressure from Hull substitute Dean Windass.
The equaliser was rich reward for Hull's perseverance - and although the Tigers have not won in five Premier League games they have at least drawn their last two fixtures.
Pompey have now taken seven points from their last seven Premier League fixtures and are still looking for their first win at home under Tony Adams.
The Portsmouth boss will be wondering how his team failed to take all three points - and Adams' team certainly made an excellent start to the match.
Diop struck the crossbar with a powerful header after just two minutes.
The ball bounced down towards the goal-line - and all eyes focused on 25-year-old referee Stuart Atwell, who correctly ruled that not all of it had crossed the line and duly waved play-on.
Further chances fell to Diop, who really should have converted from six yards after Crouch headed the ball back into his path but the Senegal midfielder missed the target.
Adams encouraged by team performance
Crouch headed wastefully over from a John Utaka cross but the tall striker made no mistake after Johnson's deflected shot fell to Kaboul and the defender crossed for the England striker to put his team in front.
Nadir Belhadj was particularly threatening for Pompey, with the visiting team struggling to contain his mazy running.
However, having offered precious little goal threat for the opening half hour, Hull almost equalised when Marlon King pounced on a loose ball and dinked his shot past David James but wide of goal.
And the Tigers were unfortunate not to restore parity when Geovanni's sensational long-range strike crashed against the crossbar on the stroke of half-time.
The equaliser did come when Kamil Zayatte flicked on a corner at the near post and Turner headed home at the far post.
It almost got even better for Hull but James made a brilliant one-handed save to deny Dean Marney.
Horton satisfied with draw
Adams tried to change things by introducing David Nugent and Armand Traore but his substitutions had nothing to do with Johnson's spectacular strike.
There seemed to be nothing on when the ball fell into Johnson's path but the England defender chested the ball and volleyed it into the top corner with his next touch while Tigers keeper Boaz Myhill stood motionless.
Myhill, though, did well to get down and save a shot from Utaka, who later missed from four yards.
Brown brought on Dean Windass and Peter Halmosi - and the former had a significant role to play in the game's final goal.
Pompey failed to clear the danger and when the ball came back into the six-yard box Windass was on hand to head it goalwards.
His effort lacked power but it bounced off Pamarot and into the net.
Portsmouth boss Tony Adams: "At the moment we are having problems locking up and winning games. Credit to Hull, they never give you a moment's peace.
"It is important that you do not lose but we did not finish them off. We had enough chances to bury them.
"But we did not get the two-goal cushion we need at home at the moment."
Hull assistant boss Brian Horton: "After going 2-1 down we would have probably taken a point.
"Dean Windass is a clever player and he knows chances are hard to come by.
"We are a little disappointed because we had some tremendous chances but then again so did they."
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