Everton continue to impress under Roberto Martinez after beating Aston Villa, while Norwich City and Cardiff City played out a scoreless draw.
Stoke were in front after just four minutes when David de Gea produced a superb stop to deny Peter Crouch, but Jonny Evans' attempted clearance hit the Stoke striker and bounced over the line.
De Gea kept United in the game with a couple more smart stops before the champions equalised two minutes before half-time when Robin van Persie finished first time after Asmir Begovic had pushed out Wayne Rooney's header.
Yet Stoke were back in front before the interval when more sloppy defending by United gave away a free-kick on the corner of the penalty area and Marko Arnautovic curled his shot in off the underside of the bar.
United had been toiling in search of an equaliser, but drew level again 12 minutes from time when Van Persie played a corner into the near post and Rooney's header looped over Begovic.
Within two minutes, United were in front when Patrice Evra fired over a cross from the left and substitute Javier Hernandez was left unmarked to head home at the far post.
Mikel Arteta opened the scoring and was later sent off as leaders Arsenal ground out a 2-0 victory over managerless Crystal Palace at Selhurst Park.
Arsenal made the breakthrough two minutes after half-time when Arteta steered his penalty beyond Julian Speroni following Adlene Guedioura's reckless challenge on substitute Serge Gnabry.
But on 65 minutes Arteta was shown a red card after the midfielder pulled back his former team-mate Marouane Chamakh just inside the Arsenal half, with referee Chris Foy deeming that the Spaniard had denied the Palace striker an obvious goalscoring opportunity.
Palace twice forced excellent saves out of Arsenal keeper Wojciech Szczesny before Arsenal killed the game off three minutes from time when Olivier Giroud headed Aaron Ramsey's pass beyond Speroni.
Liverpool took the lead after 12 minutes when Suarez received possession about 30 yards from goal, ran towards the edge of the area and nudged the ball through Jonas Olsson's legs before firing low into the corner.
Suarez increased the lead just five minutes later with a fine header from the edge of the box which flew into the top corner.
Uruguay international Suarez completed his hat-trick 10 minutes into the second half when he headed Steven Gerrard's free-kick beyond Boaz Myhill.
West Brom pulled a goal back on 66 minutes when James Morrison hammered home a penalty after Billy Jones had been pushed in the box.
But Liverpool scored a fourth on 77 minutes when Daniel Sturridge, who had rattled the crossbar earlier in the half, chipped a delightful shot over Myhill.
Romelu Lukaku showed Aston Villa what they missed out on as he scored the opening goal in Everton's 2-0 victory at Villa Park.Villa were awarded a penalty on seven minutes when Christian Benteke was clipped by Seamus Coleman, but the Belgian striker's spot-kick was brilliantly turned away by Everton keeper Tim Howard.
Everton eventually made Villa pay for that miss on 68 minutes when Lukaku, who was a target for Paul Lambert in 2012, steered his shot from the edge of the area past Brad Guzan.
With nine minutes to go, Everton scored a second when Leon Osman, who had teed up Lukaku for the opener, side-footed home from 20 yards out.
In Saturday's late game, Rickie Lambert and Jay Rodriquez both struck as Southampton produced a dominating display to dispatch a below-par Fulham 2-0 at St Mary's to climb to third in the Premier League.