The 27-year-old forward has regularly made the headlines for all the wrong reasons since he joined the English Premier League giants in 2011.
He started last season completing a 10-game ban for biting Chelsea's Branislav Ivanovic -- a punishment that came a year after he received an eight-game suspension for racially abusing Manchester United's Patrice Evra.
Even before he joined Liverpool, Suarez was dubbed "the cannibal of Ajax" when he bit an opponent's shoulder and was handed a seven-game ban.
"I'm very happy about this victory. I wanted to help the team, try to get three important points, but it's not the final word," said Suarez, who was voted player of the season by his peers in England.
"It was a dream afternoon because we won, because of the way we won, and for what the rival meant to me, for everything that was said, the doubts, and this was a way to demonstrate everything I wanted to prove."
Luis Suarez, back in action just four weeks after knee surgery, put Uruguay ahead with a 39th-minute header before Wayne Rooney equalised.
But the Uruguayan had the final say when he latched on to a long ball and smashed home the winner five minutes from time after Gerrard mistimed a header in midfield.
Suarez, who missed Uruguay's opening defeat to Costa Rica, said he was delighted to prove to his doubters he was playing at a "world-class level" despite speculation over his fitness.
And asked what he told Gerrard after the game, he said: "I said keep going and forget about this game."
England boss Roy Hodgson raised the stakes ahead of Thursday's match in Sao Paulo by insisting Luis Suarez has yet to prove he's a world class striker.
Speaking about Hodgson, Suarez said: "He sees me all year long over there. He knows what I'm worth as a player, as a person, and these things help to build courage and character going forward."
"It's a very important victory that we wanted, that we needed because we knew it was a crucial and vital game for us," he added.
"We won but we haven't qualified yet. We need to keep our feet to the ground because we have another game against Italy."