The 18-time champions, who haven't won the title since 1990, moved two points behind Arsenal after the leaders were stunned 6-3 at Manchester City on Saturday.
Defending champion Manchester United trails Arsenal by 10 points after winning 3-0 at Aston Villa to avoid a third successive league loss.
After Danny Welbeck's double for United, Suarez netted twice for Liverpool and played a part in the other three goals at White Hart Lane.
After another demoralizing collapse, Tottenham, which see itself as a Champions League team, is five points from fourth place but above United.
It is Liverpool exceeding expectations this season, sitting in second place.
The gulf between Liverpool and Tottenham, although only six points, seemed far wider on the basis of Sunday's lopsided encounter.
The contrast between the strike forces in the league is glaring.
Suarez has 17 goals in a season that only began in late September as he completed a 10-game biting ban.
Tottenham has scored only 15 times in 16 league games and couldn't even muster a shot on target against the visitors who were without the injured striker Daniel Sturridge and captain Steven Gerrard on Sunday.
Instead Suarez captained Liverpool for the first time, an unthinkable proposition when he was banned for racist abuse, then biting before agitating for a transfer in the summer window.
Suarez took just 18 minutes to open the scoring. Defender Michael Dawson blocked a through ball from Suarez, but Jordan Henderson recovered possession and fed the Uruguay striker to nip in and score.
Henderson volleyed in the second five minutes before halftime, seizing the ball after Suarez was denied by goalkeeper Hugo Lloris.
Any hopes of a Tottenham comeback were thwarted by Paulinho being sent off in the 63rd for sinking his boot into Suarez's ribs.
With a man advantage, Liverpool was even more dangerous up front.
And Suarez then crossed for Flanagan to score Liverpool's third in the 75th, found the net again himself in the 84th by chipping Lloris, and fed the ball for Sterling to complete the rout five minutes later.
"I loved our arrogance today," Liverpool manager Brendan Rodgers said. "The arrogance with the ball was very good — lots of angles, lots of people moving and interchanging positions.
"We looked a real threat whilst retaining that solidity in defensive shapes."
At Villa Park, Welbeck seized on Robin van Persie's injury absence to score his first goal since the opening day of the season in August.
Welbeck buried the rebound in the 15th minute after Adnan Januzaj headed against a post, and netted again three minutes later from Antonio Valencia's cross.
"It is really important for Danny," United manager David Moyes said. "He is a forward and he needs to get himself goals. He got two poacher types today and he could have had had another.
"With Robin out he stepped up to the mark. When you get opportunities, you show what you can do. Danny certainly did that."
Another goal drought ended, with Tom Cleverley, scoring his first goal in a year from Wayne Rooney's lay-off in the 52nd.
In the day's other game, Norwich and Swansea drew 1-1.
Nathan Dyer capitalized on some poor defending from Norwich captain Sebastien Bassong to put the Welsh side ahead in the 12th minute.
But Dyer was stretchered off before halftime with an ankle injury sustained in a challenge with Bassong.
And in first half stoppage time, Gary Hooper levelled for Norwich, lashing home from 25 yards (meters) after collecting a knockdown on his chest.