The home team took the lead after 21 minutes when Trezeguet met John McGinn’s free-kick into the area and diverted into the back of the net.
Roberto Firmino thought he had levelled shortly after, but VAR ruled the goal out due to a marginal offside call.
Liverpool toiled in search of an equaliser throughout the second half, applying heavy pressure to the home side’s goal, but had to wait until three minutes from time when Andy Robertson thumped in a Sadio Mane cross with his head.
And it was to get even better in the third minute of stoppage-time when Mane glanced a corner across goal and into the far corner to ensure the Reds’ six-point lead at the summit remained intact.
Team news
Liverpool’s teamsheet showed just one change from their last Premier League outing as Adam Lallana replaced Fabinho in midfield. Naby Keita shook off a knock sustained against Arsenal in midweek to take a place among the substitutes.
Trent Alexander-Arnold made his 100th appearance for the Reds, becoming the fourth-youngest in the club’s history to reach the landmark.
First half
Villa had made a solid start to life back in the Premier League after gaining promotion – and they could have taken the lead inside 30 seconds.
Anwar El Ghazi bundled his way into space on the edge of the area, but prodded straight at Alisson Becker from a central position.
The home team were looking sprightly, though, and after Alisson had just beaten Trezeguet to an under-hit Jordan Henderson back pass, Wesley should have done much better when he failed to connect with Matt Targett’s centre when unmarked seven yards out.
Liverpool mustered their first real threat on 16 minutes when Henderson hoisted a ball into the box that Mane nodded wide under pressure from Frederic Guilbert.
Moments later, Virgil van Dijk’s diagonal pass sent Mohamed Salah scampering into space. His shot on the half-volley from a tight angle was beaten away by Tom Heaton.
However, Villa took the lead with 21 minutes elapsed when McGinn’s dead ball from the left picked out Trezeguet’s unattended run into the area. The Egyptian steered beyond Alisson from close range, despite a hand from the goalkeeper.
Liverpool thought they had drawn level soon after, but VAR deemed Firmino offside when he tapped in from Mane’s cross.
With the interval approaching, a counter-attack from the Reds resulted in Salah scooping a pass from Mane well over the bar under the attentions of Tyrone Mings, ensuring Villa went in with a lead at the break.
Second half
Liverpool set about asserting themselves more on the contest immediately after the restart.
Firmino had a half-volley on the turn deflected over, while both Georginio Wijnaldum and Mane saw drives from the edge of the area claimed by Heaton.
The Aston Villa ‘keeper was called into action once more on 59 minutes, keeping out Mane’s back-post header at point-blank range with a sprawling stop as the Reds continued to apply pressure to their opponent’s back line.
The visitors made a double change just after the hour mark, with Divock Origi and Alex Oxlade-Chamberlain replacing Wijnaldum and Salah.
Oxlade-Chamberlain was straight into the thick of the action, having three shots blocked in succession by Villa bodies inside the box. Origi then scooped over at the near post from a corner, before Mane steered off target.
Then, on 73 minutes, Liverpool’s best chance went begging as Lallana slid wide of the far post from Firmino’s lay-off.
At the other end, a Villa counter required Van Dijk to clear from in front of the line to prevent the hosts from going further in front as Trezeguet squared for Wesley.
With time ebbing away, Alexander-Arnold sent a left-footer just wide of the far post after cutting inside.
But finally, the pressure told with three minutes of normal time remaining. Mane’s centre from the right found Robertson at the back post, who hammered a header beyond Heaton from inside the six-yard box.
Dejan Lovren then sent a glance spinning wide from a corner and Alexander-Arnold had a free-kick deflected over by a home side wall.
However, deep into stoppage-time, Mane met the resulting corner with a near-post header that found the far side of the net and sent the travelling supporters wild as Liverpool completed a dramatic turnaround.