The Cottagers needed to win their final Group E game to leapfrog the Swiss side and progress behind leaders AS Roma into the final 32.
Despite the much-needed nature of the game, manager Roy Hodgson started with Brede Hangeland, Clint Dempsey and Damien Duff on the bench.
Paul Konchesky, Chris Baird and Erik Nevland were all suspended while Andrew Johnson missed out through injury.
But despite the wholesale changes and freezing conditions in Basel, Fulham rose to the occasion and should have taken the lead early on when Danny Murphy crashed a drive from close range wide of the mark.
Zamora did have the ball in the net on 15 minutes but we correctly judged offside after latching on to Bjorn Helge Riise's through-ball.
But the big striker was not to be denied and he finally broke the deadlock three minutes before half-time.
Riise's pinpoint cross found Zamora in space in the penalty area and he converted from six yards.
One swiftly became two when Zamora doubled the advantage in first-half stoppage time.
Riise was again the architect as he was sent clear down the left by Zamora before finding the striker with a far-post cross which he headed home confidently.
Basel were gifted a lifeline in the 64th minute when Chris Smalling was harshly adjudged to have handled the ball in the box and Alexander Frei slotted home the ensuing penalty.
But Zoltan Gera settled the nerves of the visitors when he restored their two-goal advantage in the 77th minute.
Full-back Stephen Kelly pulled the ball back perfectly for the Hungary international to side-foot home a well-worked third goal.
Basel set up a grandstand finish when Marco Streller made it 3-2 in the 87th minute, but Fulham held on to ensure their name will be in he hat for the draw for the latter stages when it is held back in Switzerland on Friday.