Roberto Firmino levelled from the spot late on after Divock Origi was felled, contentiously going down belatedly, to cancel out Keidi Bare's first-half headed opener in Munich.
But Jordan Henderson missed his shoot-out spot-kick, allowing Atleti to take the lead after two penalties. It was an advantage they didn't relinquish, winning 5-4 to win the biennial tournament.
Atleti, meanwhile, travel to England to face newly-promoted top-flight outfit Brighton & Hove Albion this Sunday before kicking off their La Liga campaign at Getafe next Friday.
Changes aplenty for both sides
Atletico boss Diego Simeone made wholesale changes from the strong side that overcame Napoli on Tuesday, with former Liverpool striker Fernando Torres and talisman Antoine Griezmann both starting from the bench.
Solanke and Woodburn go close
Opportunities were sparse for either side in a cagey first-half as Atleti's second-string showed the defensive organisation and resilience of Simeone's strongest side.
Dominic Solanke - one of Liverpool's stand-out performers across the whole of pre-season - flicked a header just wide from Ben Woodburn's whipped cross into the box from the left early on.
The 17-year-old went close himself when meeting Adam Lallana's dinked cross into the back post with a flying scissor kick volley, though fired a few inches wide of the far post under pressure.
Keidi Bare heads in Atleti opener
Atleti had done little to trouble Ward in Liverpool's goal, but the opener came shortly after the half-hour mark. Augusto Fernández's cross-field pass found Šime Vrsaljko to square for Correa in space.
But with the goal agape, Correa saw his attempt superbly saved by Ward - who managed to push the shot up on to his crossbar - only for the ball to rebound kindly for 19-year-old Bare, unmarked, to head in from a few yards out.
Those changes almost had an immediate impact, Solanke controlling Henderson's low ball towards the edge of the box although Lucas Hernández stood in the way of his shot after the England youth international turned towards goal.
Reds equalise from the spot through Firmino
Liverpool struggled to pose much threat despite stepping up the tempo, Robertson's cross sliced wide by José Giménez before Klopp introduced both Ovie Ejaria and Divock Origi on 63 minutes.
The Reds saw more of the ball with Atleti content to sit men behind the ball and condense the space, swarming Liverpool players once the Merseyside outfit forced possession into dangerous areas.
Grujić should have done better from Firmino's flick in one of Liverpool's only second-half openings, though fired well over the crossbar from 20 yards before Origi drilled into the side-netting on the turn.
But in the closing stages, Origi was brought down inside the box - though going down late after Gabi's contact - and Firmino stepped up to the spot to send Miguel Ángel Moyà the wrong way.
Henderson sees penalty saved as Atleti win the Audi Cup
Liverpool battled to find a winner but Ward had to make a fine reaction save to deny Hernández after the defender had peeled in front of his marker. From the following corner, ex-Manchester City centre-back Stefan Savić then hooked just over.
Up the other end, Robertson dragged a fierce left-footed effort just wide - which meant that the winner had to be decided by a penalty shoot-out.
From the spot, Henderson was the only player of 10 to miss and Filipe Luís struck the decisive fifth attempt for Atleti to win the tournament, becoming only the third different side to do so after Bayern and Barcelona.