United ran out 4-1 winners at Fratton Park despite a spirited showing from the home side, with the visitors taking the lead from a Wayne Rooney penalty on 25 minutes. Antonio Valencia had broken away on the counter and, when he found Rooney in the area, Michael Brown brought the striker down in the area.
Portsmouth were level seven minutes later, though, when referee Mike Dean pointed to the penalty spot after his assistant spotted Nemanja Vidic tugging on Frederic Piquionne's shirt. United protested furiously, but - after missing from the spot against Stoke the previous weekend - Kevin-Prince Boateng made no mistake as he fired the ball past Tomasz Kuszczak.
But United were back ahead within three minutes of the restart when Ryan Giggs played a perfectly weighted ball into the path of Rooney, who slotted beyond Asmir Begovic. United then benefited from the third penalty of the game when Piquionne brought down Giggs just inside the area and Rooney stepped up to complete his hat-trick.
Giggs made it 4-1 when he curled a free-kick around the wall into the bottom corner. Substitute John Utaka then saw a fine effort tipped onto the bar in the dying moments to sum up an unfortunate day for Pompey's new manager.
Grant was taking charge of a team for the first time since Chelsea's dramatic penalty shoot-out defeat to United in the 2008 Champions League final.
Manchester City continued their run of draws in the league as they were held 1-1 againstHull at the City of Manchester Stadium.
City broke the deadlock on the stroke of half-time when Carlos Tevez went on the attack and supplied Shaun Wright-Phillips, whose speculative shot was diverted into the bottom corner from Anthony Gardner's head.
However, City failed to extend their advantage and they paid the price when Hull were awarded a penalty as Joleon Lescott appeared to handball before Kolo Toure brought down Jan Vennegoor of Hesselink.
Jimmy Bullard, who had scored from the spot against West Ham last weekend, smashed the ball home before the visitors celebrated by recreating the scene of Phil Brown's famous team-talk at the ground the previous season.
The result meant Mark Hughes had to settle for a point for the seventh game in succession.
West Ham came out 5-3 winners in an astonishing match against Burnley at Upton Park.
Jack Collison had put the Hammers ahead on 18 minutes as he slotted home following Scott Parker's quick free-kick, and Junior Stanislas made it 2-0 from Guille Franco's pass after half an hour.
Things got worse for Owen Coyle two minutes before the interval when Carlton Cole converted a penalty after Robbie Blake had fouled Jonathan Spector, and it was 4-0 six minutes into the second half when Stanislas turned provider for Franco as the Mexican headed home.
West Ham had their fifth on 63 minutes as goalkeeper Brian Jensen fouled Luis Jimenez in the area, and the on-loan Inter Milan attacker stepped up to extend his team's advantage. The offside flag then spared Jensen as he brought down Zavon Hines in the box, and Burnley started to make amends as Steven Fletcher was left with a simple finish from Chris Eagles' cross.
The duo repeated the feat on 68 minutes as Fletcher again scored from Eagles' cross to make it 5-2, and the drama continued into injury time. First, Steven Caldwell was dismissed for a foul on Hines, but Burnley continued to narrow the gap as Eagles made it 5-3 from Tyrone Mears' pull-back.
Fulham were forced to settle for a 1-1 draw as they hosted struggling Bolton at Craven Cottage.
Fulham had looked in control in the early stages, but Ivan Klasnic took advantage of a poor clearance from Brede Hangeland on 35 minutes to fire in a fine effort, sparking an impressive spell as they looked to extend their advantage before the break.
However, Roy Hodgson took off defender John Paintsil for midfielder Simon Davies on 68 minutes as he looked to force an equaliser and the more attacking approach paid off as Damian Duff picked up a pass from Erik Nevland out wide before firing into the far corner.
Roberto Martinez got the better of predecessor Steve Bruce as Wigan came out of their game against Sunderland at the DW Stadium with a 1-0 win.
Jason Scotland hit the post on 25 minutes, but there was little else to get excited about in a quiet first half. Yet Wigan went some way towards atoning for their record 9-1 defeat at Tottenham the previous week as Hugo Rodallega took advantage of a mistake from Paolo da Silva to get the only goal of the game.
Blackburn and Stoke played out a 0-0 draw at Ewood Park. Chris Samba had a chance to win the match in injury time as he rose to meet Morten Gamst Pedersen's corner, but he put his header wide.
