Captain Steven Gerrard scored four minutes into stoppage time to cap a thrilling 2-1 comeback victory over Middlesbrough in the Premier League on Saturday.
A header by substitute Michael Owen earned Newcastle United a 1-0 home win over Bolton Wanderers in his first game of the season while Tottenham Hotspur went down to a shock 2-1 home defeat by Sunderland, debutant Djibril Cisse netting the winner.
Substitute Mido, who netted in Boro's 2-1 victory over Spurs last weekend, put his team ahead at Anfield with a long-range strike 20 minutes from time.
Liverpool kept their fans on tenterhooks until Jamie Carragher's shot was deflected into his own net by defender Emanuel Pogatetz in the 86th minute.
Gerrard then produced a late angled strike to earn the home side a dramatic win.
Former Liverpool striker Cisse, who has joined Sunderland on loan from Olympique Marseille, sent ambitious Spurs crashing to their second successive defeat when he nodded the winner from Daryl Murphy's left-wing cross in the 82nd minute.
Sunderland had gone ahead at White Hart Lane with a brilliant 25-metre drive from Kieran Richardson before Spurs, without want-away Bulgaria striker Dimitar Berbatov, equalised through Jermaine Jenas in the 73rd.
Coach Juande Ramos left Berbatov, who has been linked with a move to Manchester United, out of his squad.
"I have not selected him as I do not think he is focused enough and I do not feel he will be good for the dressing room and the team effort," Ramos told the Spurs website (www.tottenhamhotspur.com).
"It doesn't matter how good a player is, if he is not in the right frame of mind he will not perform well."
Mali striker Mamady Sidibe struck four minutes into stoppage time as promoted Stoke City defeated Aston Villa 3-2.
Everton took more than an hour to break down West Bromwich Albion's resistance before securing a 2-1 away win while Blackburn Rovers were held 1-1 at home by Hull City.
