Portugal forward Orlando Sa had netted after just six minutes to put the visitors on course for a rare away win.
Norwich, though, continued to press and just when time was running out, Jackson nodded in Elliott Bennett's right-wing cross to earn Paul Lambert's men a deserved share of the points.
The Canaries manager had made four changes from the side easily beaten here by Tottenham on December 27.
However, his side failed to keep a clean sheet as it took only six minutes before their defence was breached.
Moussa Dembele was allowed to charge to the edge of the penalty area before feeding Sa, who drilled a low shot past John Ruddy into the bottom right corner.
The home side were almost 2-0 down before they could mount a recovery, with full-back Kyle Naughton on hand to clear an effort off the line from lively Portugal striker Sa.
Slowly Norwich managed to get some possession, and a spell of pressure saw Bradley Johnson set up just inside the Fulham box, but his sidefoot effort was deflected behind.
Fulham goalkeeper David Stockdale then knocked the ball up off the underside of the crossbar from Zak Whitbread's header, before John Arne Riise blocked Steve Morison's close-range effort.
Norwich remained on the offensive, but continued to lack a telling final pass when in promising positions.
The visitors broke quickly on 32 minutes and came close to a second goal when Clint Dempsey's close-range header cannoned back off the crossbar from a right-wing cross by Stephen Kelly.
Kerim Frei charged forwards, brushing off Daniel Ayala far too easily before rifling in an 18-yard effort which John Ruddy beat away.
When Norwich finally managed to get the ball into the Fulham half, once again there was no outlet to support Morison.
Captain Grant Holt - the club's leading scorer with seven goals - was sent on for the start of the second half, replacing midfielder David Fox as Lambert looked to inject new life into the Norwich attack.
Fulham, though, did not look too stretched by the change as Philippe Senderos and Brede Hangeland remained untroubled.
The visitors continued to counter-attack well, with Sa their main threat.
When Norwich did get a man over down the left and Morison pulled the ball back across goal, Anthony Pilkington's effort was blocked by Riise.
Naughton shaved the top of the crossbar with an angled drive when the home side pressed again as the hour mark approached.
Sa was bundled over by Ayala to give away a free-kick some 25 yards out, just right of the penalty arc. The ball was touched back to Riise to strike, but Whitbread got his body behind it.
With 20 minutes left, Lambert made another attacking change when diminutive Canada frontman Jackson came on for Morison.
Andrew Surman flashed a 20-yard drive wide as Norwich continued to press for an equaliser.
Stockdale soon had to turn away a curling effort from Jackson, before the Fulham keeper then held onto Whitbread's towering header.
To their credit, Norwich continued to press Fulham back, as Holt headed over from close range.
Then, deep into five minutes of stoppage time, the pressure finally told as Jackson nodded in Bennett's cross to snatch a point.
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