Flamini's second league goal since joining Arsenal more than two years ago came just before halftime, when he slid the ball home at the end of a neat passing move at the Emirates Stadium.
Toure added the second in the 56th minute after leading a counter-attack and fellow central defender William Gallas completed the list of unlikely scorers when he was left unmarked for an 80th minute header.
It was a precious victory for Arsenal, whose slow-starting title campaign had been checked by last Sunday's 1-0 defeat at West Ham United and a 1-1 draw with Everton.
Even so, they are still 10 points behind leaders Manchester United, who have 31, and are seven points adrift of champions Chelsea, albeit holding a game in hand.
Chelsea beat Watford 4-0 on Saturday with a Didier Drogba hat-trick while United won 1-0 at Blackburn Rovers.
Defeat for Liverpool left them drifting in mid-table and reflected a dismal away record in which they have taken only point from six games. They have scored only once on the road -- a Robbie Fowler penalty at Sheffield United on the first day of the season.
"Seasons are decided by the quality of the response your team can give to an unexpected defeat, like at West Ham," Arsenal manager Arsene Wenger told a news conference.
"I knew today would be an important game for my team for the season.
"Part of a big season is to beat the big teams, it's not all, but we have won at Manchester United and we have beaten Liverpool so tonight so we can have hope."
Liverpool coach Rafael Benitez said of his team's away record: "It's clear it's not good enough, we know we need to improve.
"You could see two different games. In the first half the team was there, creating chances...but when we conceded early in the second half there was a big difference we lost confidence."
Sunday's match quickly developed into an open attacking game with shots being freely traded as Liverpool's Dutch pair Dirk Kuyt and Boudewijn Zenden tried their luck and Arsenal's lone striker Thierry Henry was denied at Reina's near post.
Arsenal's passing had been slick since the start and it finally paid off four minutes from the break when Alexander Hleb played in Cesc Fabregas and the Spaniard's square ball was steered home by 22-year-old Flamini.
Toure made the points secure after the re-start, galloping on to Van Persie's through-ball and threading the ball beneath Reina for his first league goal since February 2004.
Liverpool nearly pulled one back minutes later when Zenden sent a powerful header over the bar from a Gerrard free kick.