Jimmy Bullard and Clint Dempsey worked effortlessly to turn the tide and push Fulham forward.
Vennegoor of Hesselink then slotted home at the death after Thomas Sorensen failed to hold Jimmy Bullard's shot.
Clint Dempsey forced Hart into a diving save from Simon Davies's pull-back after Jimmy Bullard's long-range effort dipped wide.
Soon after, Fulham's John Pantsil followed through on keeper Robert Green who had bravely palmed Jimmy Bullard's low free-kick away.
Gomes pushed away a thunderous 25-yard free-kick through a crowd of players from Jimmy Bullard and held on to a low Davies drive from similar range.
Fifth-placed Aston Villa moved level with Tottenham on 26 points after winning 3-0 at home to Hull, who lost influential midfielder Jimmy Bullard to yet another knee injury.
The Gunners took the lead through Andrey Arshavin after 14 minutes but Jimmy Bullard leveled with a penalty after 28 minutes when Sol Campbell fouled Jan Vennegoor of Hesselink.
Moments later, Town's veteran midfielder Jimmy Bullard hit a shot which flew narrowly wide from 30 yards before team-mate Carlos Edwards hit a fierce 35-yard effort which went over the crossbar.
It was a much-needed three points for the Tigers after three straight defeats and they were also boosted by the appearance of midfielder Jimmy Bullard for the first time this season.
Hodgson has harnessed the composure of veteran Danny Murphy in midfield and this, coupled with the return from injury of key duo Jimmy Bullard and Brian McBride, has proved the catalyst for recovery.
Hull had gone into the match without Jimmy Bullard as boss Phil Brown decided to rest his star man so that the midfield playmaker could recover from a minor knock to his knee.
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