Raheem Sterling, Steven Gerrard and Alberto Moreno scored the goals for Liverpool at White Hart Lane to give Brendan Rodgers victory in his 100th game as manager and end Tottenham's 100 percent record.
"Overall our quality was exceptional. We got three goals and could have had more," said Rodgers.
Mario Balotelli made his Liverpool debut after his pound sterling16 million ($26.5 million, 20.1 million euros) move from AC Milan on Monday and he produced an enterprising display before being withdrawn in the 61st minute.
"I thought he was excellent," Rodgers said of the maverick striker.
"He's bought straight into our team ethic. He's trained well and has put all that background noise about him to one side. He's been brilliant."
The result saw Liverpool bounce back from a 3-1 defeat at Manchester City in their previous outing and means they have now scored 12 unanswered goals in their last three encounters with Spurs.
After former City striker Balotelli had tested Hugo Lloris with an early header, Liverpool went ahead in the eighth minute.
Daniel Sturridge released Jordan Henderson with a ball down the right flank and the England midfielder played a low cross across the box that Sterling tucked away at the far post.
Gerrard doubled the visitors' lead from the penalty spot in the 49th minute after Eric Dier had held back Joe Allen and Moreno sealed victory on the hour with a memorable first Liverpool goal.
The Spanish left-back, a close-season arrival from Sevilla, dispossessed Spurs substitute Andros Townsend on halfway and surged into the box before drilling a shot into the bottom-right corner.
"We need to learn and improve," said Spurs coach Mauricio Pochettino. "Today was a very tough game for us."
With Olivier Giroud sidelined by a broken tibia, Yaya Sanogo started up front for Arsenal at promoted Leicester and he played a central role in the visitors' 20th-minute opener.
The French striker could not find a way past Kasper Schmeichel from Santi Cazorla's dinked pass, but Alexis Sanchez followed up to slam home his first league goal since signing from Barcelona.
Arsenal's lead was to last only two minutes, however, as Jeff Schlupp motored down the left wing before delivering an inviting cross that Leonardo Ulloa powered past Wojciech Szczesny with a firm header.
Arsenal centre-back Laurent Koscielny hurt himself in a clash of heads with Schlupp when the score was still 0-0 and he made way for Calum Chambers shortly after Ulloa's goal.
Leicester came closest to scoring a winner in the second half, but Ulloa clipped an effort into the side-netting after cutting inside Chambers while Szczesny produced a diving save to thwart substitute Jamie Vardy.
"It was tough. Leicester played very well and defended with a lot of heart," Arsenal manager Arsene Wenger told Sky Sports.
Asked if he would look to bring in a replacement for Giroud before the transfer window closes on Monday night, he added: "We are active in the window. We are working hard to find a solution."
The result left Arsenal four points below leaders Chelsea in seventh place in the table, while Leicester moved up to 15th.
In the day's other game, Aston Villa won 2-1 at home to Hull City to maintain their unbeaten start to the campaign and climb to third place.
Gabriel Agbonlahor and Andreas Weimann put the hosts two up at half-time at Villa Park, with Nikica Jelavic replying for previously unbeaten Hull in the 74th minute.
Chelsea will go into the international break above Swansea City on goal difference at the top of the table after an engrossing 6-3 win at Everton on Saturday, in which new striker Diego Costa scored twice.
Mame Biram Diouf claimed the only goal as Stoke City pulled off a surprise 1-0 win at Manchester City, while Angel di Maria made his debut for Manchester United in a 0-0 draw at Burnley.