Adam put the hosts in front with a deflected effort, then smashed home an excellent second to settle the 2-1 victory after Robin van Persie had levelled straight after the break.
It was the first time United had tasted defeat at the Britannia Stadium too, their eighth reverse of the campaign dealing a savage blow to their hopes of securing a UEFA Champions League berth for next season.
Earlier on Saturday, Alan Pardew was left alone to face a furious backlash as Newcastle succumbed to another humbling derby defeat by Sunderland.
Fans incensed by the club's decision to sell Yohan Cabaye and not replace him vented their anger on Pardew as the Black Cats cruised to a second successive 3-0 victory at St James' Park.
Everton bounce back
Late goals from Steven Naismith and Kevin Mirallas helped Everton bounce back from their Merseyside derby drubbing by Liverpool with a 2-1 victory over Aston Villa at Goodison Park.
Leandro Bacuna gave Villa a shock lead but Everton ramped up the pressure in the second half and got their reward when Naismith struck 16 minutes from time.
Cardiff's new boys made an instant impact as Wilfried Zaha and Kenwyne Jones enjoyed dream debuts in a 2-1 win over Norwich.
But substitute Zaha teed up Craig Bellamy for the equaliser just after the break, with Jones firing home the winner at the second attempt just over a minute later.
Andy Carroll twice set up goals for Kevin Nolan before being sent off as ten-man West Ham beat Swansea to ease their relegation predicament.
The England striker twice provided cushioned headers for Nolan to score in a 2-0 win at Upton Park but later received a straight red card for an altercation with Chico Flores. West Ham have immediately appealed against the dismissal.
Shane Long's first goal for Hull saw them claim their first point of the year from a 1-1 draw which ended Tottenham boss Tim Sherwood's perfect away record in the league.
Former West Brom striker Long put the Tigers ahead 12 minutes into his home debut but Paulinho's powerful 61st-minute strike drew Spurs level and salvaged a share of the spoils.
Recent arrivals Lewis Holtby and William Kvist started for the Cottagers but were unable to stop their new club slipping to the bottom of the Premier League table.