Villa looked set for a fourth consecutive defeat in all competitions as an Emiliano Martinez own goal and strikes from Cody Gakpo and Jarrell Quansah put the visitors on course for victory in Jurgen Klopp’s final away game in charge.
But substitute Duran’s double edged Unai Emery’s men closer to Europe’s top table for the first time since 1983.
Victory for title-chasing Manchester City at Spurs on Tuesday would secure Villa’s place in the top four.
But they are stumbling over the finish line as the strain of combining a challenge for the Champions League alongside a run to the Europa Conference League semi-finals has taken its toll.
Martinez’s return to fitness after he missed last weekend’s 1-0 defeat at Brighton should have been a major boost for the home side.
But the Argentine World Cup winner’s howler handed Liverpool the opening goal after just two minutes as he fumbled Harvey Elliott’s deflected cross into his own net.
Villa did respond positively as Ollie Watkins burned Quansah for pace and pulled back a cross for Youri Tielemans to equalise.
However, momentum swung back in Liverpool’s favour in an end-to-end encounter when Gakpo tapped in after Martinez could only parry Joe Gomez’s effort.
The outcome for the home supporters could have been much happier had their players not frequently contrived to get in each other’s way.
Diego Carlos somehow turned wide with the goal gaping after nudging Watkins out the way.
Villa’s struggles defending cross balls have been a consistent factor in a run of poor results in recent weeks.
It was exposed again as Liverpool struck within three minutes of the restart for the second half when Quansah rose highest to head in Elliott’s free-kick.
There was still time for Villa to mount a memorable comeback had they been more ruthless as Liverpool’s own defensive weaknesses were laid bare.
Watkins was denied his 20th Premier League goal of the season after Leon Bailey ran offside in the build-up, having cut across the run of Moussa Diaby.
After an angry exchange of words between Bailey and Watkins, it was then the latter who was guilty of getting in Douglas Luiz’s way when the Brazilian would have had a clear sight of goal.
Had it not been for an injury to substitute Nicolo Zaniolo, Duran may not even have entered the field.
But the Colombian produced a stunning finale as he pounced on a mistake from Alexis Mac Allister to drill home from the edge of the box.
Duran did not know much about his second as Diaby’s pass ricocheted in off his thigh, but Hollywood star and Villa fan Tom Hanks was one of the 40,000 who did not care.
Only a brilliant save from Alisson Becker denied Diaby a winner in stoppage time.
A point for Liverpool may be meaningless in their quest to win the title as wins for Manchester City and Arsenal over the weekend mathematically ended the chance of Klopp departing as a Premier League winner.
Yet, it could still be significant in the title race as it keeps Tottenham’s chances of Champions League football alive ahead of City’s trip to north London on Tuesday.
Even if Spurs spring a huge surprise, Villa still have a top-four finish in their hands when they visit the in-form Crystal Palace on the final day of the season on Sunday.
Villa’s eight-goal superior goal difference means a draw at Selhurst Park should be enough even if Tottenham win in their two final matches against City and relegated Sheffield United.
