Australia's Richard Green finished second at 9-under 279, one shot ahead of England's Nick Faldo.
Atwal started the day one ahead of Nick O'Hern of Australia and quickly distanced himself from the rest of the field with three birdies on the front nine to make the turn at 13-under.
The 28-year-old added another birdie at the par-5 11th and cruised at even-par the rest of the way.
'It's quite an achievement to be the first Indian golfer to win on the European Tour,' said Atwal, who joined Jeev Milka Singh as the only Indians to earn full membership on the tour after graduating from the European Q-School last November. 'Jeev has come close, finished second and third in South Africa. I didn't expect to win so quickly but I will take it.'
Atwal joined Japan's Isao Aoki and Taiwan's Lu Liang-Huan and Yeh Wei-tse as the fourth Asian golfer to win on the European circuit.
'Hopefully it will do wonders for golf in India,' said Atwal. 'We have had a bunch of guys who have won on the Davidoff Tour but to win on the European Tour is a totally different ball game. Hopefully it will show all the young kids who have started playing seriously in India and are thinking of turning pro that there is a future in golf for them.'
Green provided a short-lived challenge to Atwal after a short birdie at the first and another at the seventh to climb to 8-under. However, it was not enough to overcome the eventual winner.
'It was probably better than expected,' said Green, who posted his best finish since capturing the 1997 Dubai Desert Classic. 'I hadn't been playing that great in Australia but things have been turning around. I had a few chances today. I made probably two mistakes which I thought cost me. You always want a chance to win and I gave it a good shot but it was Arjun's day.'
Faldo (70) used a stretch of four consecutive birdies from the 11th to post his best finish since the 2001 Volvo PGA Championship.
'It's nice to be up there,' he said. 'It's good for me to play under pressure. I have found what works at the weekend when I am under pressure and have to keep working on those feelings, The more I can groove those and get that little bit more confidence, the better.'
American Ted Purdy (73) was joined by Thailand's Thavorn Wiratchant (72) in a tie for fourth at 7-under 281.
A group of four finished at 6-under 282, including Sweden's Richard S. Johnson, last week's winner at the ANZ Championship. He was joined by South Africa's James Kingston (70), Chris Williams of England (71) and American Jim Johnson (74).
This event is co-sanctioned by the European and Davidoff Tours.
Full-field scores from the Singapore Masters