The Colombian, brought on at half-time by Felix Magath, glanced in Lewis Hotlby's right-wing cross four minutes from time to earn Fulham a priceless three points in their battle to avoid relegation.
They had earlier taken the lead through Kieran Richardson's wonderful strike just after the hour, the former Sunderland man running on to substitute Askhan Dejagah's pass and lashing a first-time strike into the top right-hand corner from 20 yards.
Nine minutes later, Villa's on-loan Wigan Athletic striker Grant Holt, selected in place of the injured Christian Benteke, looked to have earned his side a point when he headed in a 70th-minute equaliser from Marc Albrighton's corner.
But Magath had targeted four wins from Fulham's final six matches to beat the drop, and Rodallega's header will come as a massive lift as the visitors won in the league at Villa Park for the first time since 1970.
It looked as though they would have to settle for a point when Matthew Lowton somehow stretched to clear Holtby's close-range effort off the line at 1-1, with the goal decision system ruling that only a tiny portion of the ball had not crossed the line.
But Rodallega's late intervention, securing a first away Premier League win since Boxing Day, re-ignites Fulham's chances of avoiding the drop, as they now sit 18th.
After a quiet opening, the visitors wasted a presentable opportunity to take the lead in the 20th minute.
Nathan Baker squandered possession deep inside the Villa half, but Cauley Woodrow waited too long to slip the ball to Pajtim Kasami, who had to stretch to stab an effort forward and the attack came to nothing.
Andreas Weimann glanced a header narrowly over the angle of post and crossbar seven minutes later as the hosts responded strongly, with David Stockdale then parrying away Leandro Bacuna's driven effort after the Dutchman jinked into the area on the half-hour mark.
Suddenly the game became open, Woodrow taking advantage of Joe Bennett's under-hit pass to streak clear 10 minutes before the break, but his low strike from an angle was palmed away from danger by Brad Guzan.
The visitors finished the half the stronger, Holtby and Steve Sidwell both bringing saves out of Guzan from distance in the closing moments.
Bacuna went close to breaking the deadlock three minutes after the interval, seeing his fierce strike touched onto the near post by Stockdale and behind for a corner.
Richardson then gave his side the lead, crashing the ball home from just outside the area after being teed up by Dejagah.
The lead lasted just nine minutes, however, Holt left all alone to convert Albrighton's right-wing corner with a firm header.
The hosts were buoyant, Albrighton testing Stockdale with a stinging drive five minutes before Lowton's incredible goalline clearance denied Holtby, who had rounded Guzan, immediately afterwards.
As the game became stretched, Aleksandar Tonev saw his curling effort brilliantly tipped away by Stockdale at full stretch before Weimann glanced a header narrowly over the bar.
There was to be one final moment of drama, though, as Rodallega headed home to spark jubilation among the 3,000-strong visiting support.
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
