Arsenal preserved its four-point lead as Nicklas Bendtner capitalized on a rare start to score in a 2-0 win over Hull, while Eden Hazard capped a brilliant performance with two goals in Chelsea's wild 4-3 victory at Sunderland.
Manchester City stayed third by beating West Bromwich Albion 3-2, mainly thanks to Yaya Toure's brace, but the star of the night was Suarez, whose four goals in a 5-1 thrashing of Norwich included a 45-yard looping volley as part of a first-half hat trick.
"Just the fear he puts in defenders — the quality of his finishing is phenomenal," Liverpool manager Brendan Rodgers said of the Uruguay striker, who has now scored 11 goals in his last four games against Norwich.
While the front runners were all winning, United slumped to a fourth defeat of a turbulent first season in charge for David Moyes, whose old club of 11 years claimed a first win at Old Trafford since 1992 thanks to Bryan Oviedo's 86th-minute goal.
"It's a big catch-up for us now," said Moyes, whose team dropped to ninth place in the stuttering defence of its title — 12 points behind Arsenal after 14 games.
Tottenham ruined Rene Meulensteen's first match in charge of Fulham by winning 2-1 at Craven Cottage, giving Spurs manager Andre Villas-Boas a first win in five games and some much-needed breathing space.
Swansea ended Newcastle's four-match winning run with a 3-0 victory and Aston Villa upset Southampton 3-2 to take the number of goals in the night's nine matches to 32. Stoke was held 0-0 by Cardiff.
Suarez became the first player to score three hat tricks against the same team in the Premier League, beginning his virtuoso performance in the 15th minute with a dipping volley from long range.
An instinctive second was followed by a classy third, when he turned this way and that before smashing a rising shot into the corner from the edge of the area. He finished off his one-man show with a curling free kick and added an assist for good measure, setting up Raheem Sterling for Liverpool's fifth.
Despite missing Liverpool's first five games of the campaign to complete a ban for biting carried over from last season, Suarez is now the Premier League's top scorer with 13 goals in nine matches.
"I wish Suarez would just leave us alone!! Big bully!" Norwich midfielder Anthony Pilkington tweeted.
Arsenal may not have racked up the goals but the win was just as routine against a team that shocked Liverpool three days earlier, keeping Arsene Wenger's side out in front.
Bendtner was handed his first Premier League start since March 2011, with Olivier Giroud given a rest, and the forgotten man responded by heading home the opener after just 90 seconds.
"When he is physically sharp, he can compete with anybody," Wenger said of the Denmark striker, who has been loaned out to Sunderland and Juventus in recent seasons. "When he has that commitment and attitude, his quality shows."
Mesut Ozil stroked home a pass from Aaron Ramsey to make it 2-0 in the 47th and secure Arsenal's 11th win of the campaign.
Chelsea and Man City kept the pressure on Arsenal with entertaining away wins, with that trio looking increasingly likely to be battling for the title come May.
Hazard set up Lampard for Chelsea's equalizer, after Jozy Altidore put Sunderland ahead early, and then scored twice himself to earn plaudits from his manager, Jose Mourinho.
"Eden Hazard was excellent," Mourinho said. "He told me at dinner last night, 'Boss, for a long time I haven't scored.' He decided he would score tonight."
Sunderland defender Phil Bardsley scored at both ends in the final 10 minutes, with his team staying rooted to the bottom — two points behind Crystal Palace.
City finally found a cure to its away problems, grabbing just its second victory in seven matches on its travels thanks to Sergio Aguero's ninth-minute opener and goals by Yaya Toure either side of the break. West Brom scored twice in the dying stages via Costel Pantilimon's own goal and Victor Anichebe's injury-time strike.
With the top four all picking up three points, United chose the worst time to expose its vulnerabilities as Everton achieved under Roberto Martinez what Moyes failed to do in 11 years at Goodison Park — a win at Old Trafford.
United struck the goal frame twice, through Wayne Rooney and Danny Welbeck, but Everton overran the hosts in midfield and deservedly prevailed thanks to Oviedo's close-range finish.
"We will need to play some great football and win an awful lot of games in the run-in if we going to be in there and around it come the end of the season," said Moyes, who was jeered by Everton's travelling support throughout.