They finally grabbed the lead when Marney finished impressively after some great build-up play from Eagles.
Dean Marney sidefooted a shot across goal after Jaaskelainen spilt a Geovanni shot as Hull continued to attack.
The Tigers had the better of the second-half chances with Craig Fagan and Dean Marney both going close.
The Toffees fell behind when Stephen Hunt, Andy Dawson and Dean Marney scored for Hull in the first 28 minutes.
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Dean Marney volleyed just wide and then drilled one over the bar as the home side picked up the pace.
And Arbeloa had to clear a goalbound Dean Marney header as Liverpool continued to give Hull plenty of reason for optimism.
The Latics were on top after the break but Vennegoor of Hesselink met Dean Marney's corner to head Hull in front.
Former Canaries loanee Dean Marney had given the hosts a lead on 33 minutes after good work by winger Chris Eagles.
Distin inadvertently diverted a low cross to Marney and, symbolic of Everton's fortunes, the Hull midfielder's shot went in off Tim Cahill.
The hosts twice hit the woodwork through Gareth Bale and Jonathan Woodgate before the break, while Hull's Dean Marney also hit the post.
Soon after, Marney latched on to a fine throughball from Geovanni but dragged his shot across the face of the goal and inches wide.
Hull deserved their point and could have come away from Stamford Bridge with all three had Craig Fagan and Dean Marney not missed second-half chances.
Andy Dawson's free-kick and a Dean Marney shot added to the lead but Hull's Kamil Zayatte sliced a clearance into his own goal to give Everton hope.
Another incisive move ended with former Spurs midfield man Marney beating Gomes with a shot on the turn, only to see his effort rebound to safety off the post.
That all changed on the hour mark when Vennegoor of Hesselink met Marney's corner with a fierce downward header for his first goal since joining the club at the start of September.
Downing cut inside after being put through on the left flank but his low shot was kept out by Duke but Hull responded with a Dean Marney header which was just too high.
Marney fired straight at Chris Kirkland after finding space on the edge of the area, while Barmby failed to connect properly with a volley after Hunt found him running into the area with a searching ball.
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