Rodallega had failed to hit the back of the net since September, but the striker finally notched only his second goal since his pre-season move from Wigan with a second half header to kill off the Magpies.
It was sweet relief for both Rodallega and Fulham boss Martin Jol, whose struggling side had blown the first half lead given to them by Steve Sidwell.
Although Hatem Ben Arfa equalised for Newcastle early in the second half, Alan Pardew's team, were unable to avoid a fifth defeat in their last six Premier League matches.
They remain only four points above the relegation zone after a 14th successive away match without a win.
For Pardew, celebrating two years in charge of Newcastle, it was a miserable anniversary as Fulham took control on a freezing night on the banks of the River Thames.
Rodallega had the first sight of goal for the Cottagers with a bicycle kick, although his acrobatic effort failed to test Newcastle goalkeeper Tim Krul.
Newcastle's defence was far too open and the hosts were able to exploit those gaps to take the lead and end a five-hour goal drought in the 19th minute.
Damien Duff was the provider as he released Sidwell into the penalty area and the former Chelsea midfielder's strike looped past Krul via a deflection off Mike Williamson.
Dimitar Berbatov should have doubled Fulham's advantage moments later when he surged through on goal but, with just Krul to beat, the former Manchester United forward shot too close to the Newcastle goalkeeper.
Berbatov threatened again after Krul could only palm Sascha Riether's cross to the Bulgarian, but once more he was unable to convert the chance as the Newcastle keeper recovered to save.
Pardew's team had more menace about them in the second half and French forward Ben Arfa, back from four matches out with an injury, produced a moment of inspiration to equalise in the 54th minute.
Fulham goalkeeper Mark Schwarzer must have felt relatively comfortable when Ben Arfa took possession just outside the right edge of the penalty area.
But the Australian was left flat-footed as Ben Arfa rifled a fine strike into the roof of the net via a deflection off John Arne Riise.
Krul was quickly off his line to block when Sidwell went charging through soon after, yet Fulham didn't have to wait long to take the lead.
In the 63rd minute, Duff whipped a teasing cross into the six-yard box, where Rodallega got in front of Fabricio Coloccini to head powerfully past Krul.
Desperate to make amends for that mistake, Coloccini went forward and smashed a shot against the bar from the edge of the area, but that was as close as the visitors came to an equaliser.
Source: AFP
Source: AFP