In the final 18 holes, Westwood shot 5-under 67 to end with an overall score of 20-under 268.
"I never really thought about going so long without a win," Westwood said after ending a four-year victory drought. "I've still been playing pretty well. I knew that winning is fickle -- sometimes you just don't get across the line first."
Westwood, a five-time Ryder Cup member, won 16 times between 1996 and 2003 -- including six victories in 2000 to match the European Tour record set by Seve Ballesteros, Nick Faldo and Colin Montgomerie.
Andersson (66) and Archer (65) finished at 18-under 270.
Second-round leader Louis Oosthuizen of South Africa (69) and Sweden's Michael Jonzon (69) shared fourth place at 16-under 272.