After the break Kettering maintained their positive intent, Gareth Seddon shooting wide, though Harper needed to be alert in the Kettering goal when a long-range shot kept surprisingly low and bounced clear off his shins.
Kettering conjured up more chances when Richard Graham's ball across the area deflected off Hangeland and trickled agonisingly wide.
Acting skipper John Dempster then headed a glorious chance over the bar from the six-yard line, and grimaced as he reflected on his wasted opportunity.
Westcarr hit a first-time shot straight at Mark Schwarzer as the home crowd taunted Fulham.
The Premier League side still threatened on occasions, however, Harper clearing the danger with a fine save after Paul Konchesky fizzed a shot towards the top corner.
Fulham brought on Danny Murphy and Zamora in their quest to overcome Kettering's verve, but again it was Westcarr who was providing the menace, just failing to apply the crucial touch to another chance.
Murphy broke clear to cross, but an unmarked Zamora could only head across the goal.
The visitors took the lead, however, in fortuitous fashion when the ball deflected in off Geohaghan.
Kettering hit back five minutes later when Westcarr slid home from the penalty spot after being tripped by Hangeland.
However, with the home fans making plans for a trip to London, Johnson capitalised on uncertainty at the back and Zamora finished it two minutes later.
Kettering manager Mark Cooper:
"The players are sick. They're gutted. They should have won. They deserved to win but it's a cruel, cruel game.
"We missed numerous chances. But it was an unbelievable performance against a Premier League side. It will be a long time before another non-league team puts in a better show against the big boys.
"It shows the cup is not about Manchester United against Tottenham and Cardiff against Arsenal. It's about non-league teams on their own ground taking on the big boys."
Kettering striker Craig Westcarr:
"We're all proud even though we let ourselves down in the last five minutes.
"We're quite happy. We've fulfilled our dream but we are also annoyed with ourselves. But it was a great occasion and a great atmosphere."
Fulham boss Roy Hodgson:
"A draw here would have been a defeat in our minds. But the players showed they have enough fight and character to come back and win a game when at 2-2 we were fearing the worst.
"Kettering put us under a lot of pressure and there was always the danger that we might make a mistake but I think we were good value for our four goals.
"We've still had just one defeat in 13 and we have to take a lot of pride from that. The players had to dig deep and while it wasn't the fun occasion some might have dreamt of, it was a thoroughly professional performance.
"Anything other than professional preparation could have seen an upset on the cards."
Kettering: Harper, Eaden, Geohaghan, Dempster, Jaszczun (Potter 71), Bennett, Boucaud, Solkhon, Richard Graham (Marna 89), Westcarr, Seddon (Beardsley 73).
Subs Not Used: Wrack, Galbraith.
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