United led through Juan Veron but Kevin Nolan’s equaliser and a Michael Ricketts shot, after another United defensive blunder six minutes from time, gave Bolton their shock success and a first win in seven league games.
The result allowed Arsenal to go top of the table despite being held to a 3-3 draw by Blackburn Rovers in a fantastic game at Highbury.
United eventually made the breakthrough after 25 minutes when, with David Beckham in the stands, Veron seamlessly took over the free kick duties to lash one in from 25 metres.
In a rare attack Bolton levelled 10 minutes before the break with a good shot by Nolan from the edge of the box after a clever knock-down by Ricketts.
Ole Gunnar Solskjaer then had a goal disallowed for offside and goalkeeper Jussi Jaaskelainen produced a fantastic save to deny Andy Cole just before the break.
Bolton grew in confidence in the second half and, after surviving good close efforts by Cole and Solskjaer, Ricketts robbed Wes Brown outside the box before lashing in the winner.
It was only the second time since the start of the premier league in 1992 that United had lost a match they scored first in. The only other occasion was at Tottenham Hotspur in 1999.
Arsenal, as so often this season, dominated the possession but could not turn it into goals and they were punished four minutes before halftime when Blackburn winger Keith Gillespie cut in from the right and unleashed a shot that was deflected past Richard Wright.
Arsenal turned things round with two goals in the first seven minutes after the break, Robert Pires and Dennis Bergkamp on target, but David Dunn beat Wright from distance to level.
Brad Friedel then made three good saves before being beaten by Thierry Henry, only for Dunn to volley his second into an empty net from 30 metres after Wright had been stranded making a save.
There were no such problems for Liverpool as Fowler opened his premier league account in style with a hat-trick.
Two in the first half, either side of a header for Sami Hyppia, had Liverpool cruising and after Dennis Wise pulled one back for the hosts, Fowler finished them off with a fierce volley.
English league results
PREMIER LEAGUE
Arsenal 3 Blackburn Rovers 3
Derby County 1 Charlton Athletic 1
Everton 3 Aston Villa 2
Leicester City 1 Liverpool 4
Manchester United 1 Bolton Wanderers 2
West Ham United 2 Southampton 0
Playing on Sunday: Fulham v Ipswich Town (1200 GMT kickoff) Leeds United v Chelsea (1500) Newcastle United v Tottenham Hotspur (1300)
Playing on Monday: Middlesbrough v Sunderland (1900)
GERMAN FIRST DIVISION RESULTS
Bayern Munich 4 Kaiserslautern 1
Bayer Leverkusen 4 VfB Stuttgart 1
Schalke 04 1 TSV 1860 Munich 0
Hertha Berlin 3 Werder Bremen 1
Nuremberg 1 Borussia Moenchengladbach 2
Hansa Rostock 3 Cologne 0
St Pauli 4 Energie Cottbus 0
Playing on Sunday: VfL Wolfsburg v Hamburg SV Borussia Dortmund v SC Freiburg
RESULTS OF SCOTTISH LEAGUE:
Premier league
Aberdeen 3 Dunfermline Athletic 2
Celtic 5 undee United 1
Dundee v Motherwell postponed Kilmarnock 1 Livingston 5
Playing Sunday: Hibernian v Hearts (1400 GMT kickoff) St Johnstone v Rangers (1400).—Reuters