The 30-year-old Australian, who shot a 3-under 68 in the final round for a 16-under 268 total, was surprised his final shot went in.
'It was tracking the hole all the way but I thought it was coming up short. But the breeze took it in,' said Rumford, who last won at the 2004 Irish Open. 'My short game has pulled me through this week.'
Archer, who shot a 65, had a shorter chip in the playoff but left it wide.
'Brett played well all week and is a worthy winner,' said Archer, who has never won on Tour. 'He has one of the best short games out there and I knew his chip would be close and it went straight in the middle.'
Archer is known for missing a 7-foot putt on the last hole of the 2006 Wales Open that would have given him the first 59 in European Tour history.
Defending champion Bradley Dredge shot a 69 to finish third, one shot behind Rumford and Archer. Sion Bebb had a 68 and was fourth, another stroke back.
'It had been a pretty tough year,' Rumford said. 'I just had to have five minutes alone and it has just hit me. I have been trying hard, grinding week in, week out for not much and it has all come together this week.'
The tournament was the first qualifying event for the 2008 European Ryder Cup team. Of the five 2006 team members playing, Lee Westwood was the highest finisher in a tie for sixth.
Robert Karlsson was 12th and Paul Casey was 37th, while Darren Clarke and David Howell missed the cut.