Maarten Lafeber, the overnight leader, managed a 1-over-par 73 to finish in a tie for third place with South African Trevor Immelman and American Andrew Pitts. The trio finished play at 12-under-par 276.
Harrington birdied the second hole to match Lafeber in first place at 13-under par but the Irishman pulled away from the field later in the front nine. Harrington birdied three holes in a row, starting at the fifth to reach 16-under par and grab a three-shot lead over Pitts.
Randhawa soared up the leaderboard with six birdies in his first 11 holes to take over Pitts' spot in second place, three behind Harrington. Randhawa birdied No. 15 to get within two shots off the lead where he and Harrington stayed until Harrington reached the back nine.
Harrington parred six consecutive holes on the back nine until he came to the par-4 17th. The Irishman bogeyed the hole to fall to minus-15 but it would not matter as Randhawa was in the clubhouse at 14-under par.
Lafeber and Immelman were on the course with only the 18th to play and two shots off Harrington's lead. Neither holed their tee balls at the par-3 closing hole so Harrington walked off with European Tour victory No. 6.
For Randhawa, the 2001 Davidoff Tour Order of Merit champion, the second-place turn marked his highest finish on the European Tour.
'Looking back, my 75 in the second round hurt a bit,' said Randhawa, who fired a final-round 64. 'But at least I shot a 64 today, so I'm happy. Today was just a fabulous ball-striking day. Everything was perfect.'
Lafeber had a piece of the 54-hole lead three times in 2002 but has yet to visit the winner's circle on the European Tour.
'I played good but I just couldn't hole a putt,' said Lafeber. 'So it's over.'
Ian Woosnam (70), Daniel Chopra (67), Rick Gibson (68) and Soren Hansen (69) shared seventh place at 10-under-par 278.
John Daly, who is honoring his late mother's wishes by continuing to play this week after her death on Thursday, shot his second 2-under 70 in as many days to join a large group in a tie for 30th at minus-4.
Sam Torrance, the 2002 European Ryder Cup captain, tied for 21st at 6-under par. Jarmo Sandelin, last year's Asian Open champion, tied for 24th at 5-under par in his title defense.
Jose Maria Olazabal, a two-time Masters champion, tied for 41st at minus-2.
The Asian Open was the first tournament on the 2003 European Tour schedule and was co-sanctioned by the European Tour and the Asian PGA Tour or the Davidoff Tour.
Final scores from the BMW Open