Liverpool boss Jurgen Klopp admitted there was an element of luck about his side's two late goals at Aston Villa but felt the dramatic victory that they brought was deserved.
Headers from Andy Robertson and Sadio Mane - the latter coming four minutes into injury time - maintained the Reds' unbeaten start to this league season.
They also ensure that Klopp's side retain their six-point lead at the top of the table before next weekend's mouth-watering top-of-the-table clash with Manchester City, the side that pipped them to last season's title.
"We made it hard for ourselves," said Klopp.
"Villa was ready to play for a proper fight, a proper battle, defend with all you have, try to find counter-attack opportunities. We conceded a goal and then it is hard to change this wrong path and wrong decisions immediately.
"It is lucky to score these goals of course, but when you look at the game, if either side deserved to win it is us.
"We still need to learn and get better. Sometimes you need to get knocks and today we got knocks. For really little mistakes we got really big knocks but at the end we could sort it."
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Liverpool were uncharacteristically ragged at times at Villa Park, failing to exert the authority that had seen them accrue an unmatched 28 points from the first 10 games of the season.
Despite an overwhelming share of possession, they struggled to respond to Trezeguet's 21st-minute opener for an impressive home side, with Adam Lallana, Mohamed Salah and Mane all wasteful.
But the Reds have developed a supreme ability to score late goals and they were not to be denied, with Robertson's back-post header and Mane's glancing effort from Trent Alexander-Arnold's corner the latest additions to the Reds' late collection of goals.
In the last few weeks alone Liverpool demonstrated that they are never out of a contest.
They also netted in injury time on Wednesday to secure a 5-5 draw in a remarkable Carabao Cup tie with Arsenal, which they would went on to win on penalties.
And who can forget last season's Champions League semi-final, the first leg of which Liverpool lost 3-0 at Barcelona before winning the second 4-0 at Anfield, with Divock Origi's deciding goal coming in the 79th minute.
"We have showed our resilience over the last 18 months and this season we have kept on going," said Robertson.
"Today we knew we had some great chances and there's nothing better than a last-minute winner."
Mane added: "Today was not our best performance but we deserved the three points.
"It was a perfect delivery from the corner and in the end I was even a bit lucky the ball went in.
"Aston Villa have been the team that pushed us harder so far, that's why this is the best league in the world. Every single game can be like this one."