The world number four Indian took 56 minutes to see off Lan 21-18 13-21 21-16 in the first round of the women's singles. Saina will now take on Chinese Taipei's Shao Chieh Cheng in the second round tomorrow.
Compatriot P Kashyap, however, suffered defeat in the opening round, going down in straight games to world number eight Sung Hwan Park in the men's singles.
The Commonwealth games bronze medallist lost 15-21 14-21 to the Korean in a 44-minute match.
Commonwealth Games gold medallist pair of Jwala Gutta and Ashwini Ponnappa also failed to cross the first hurdle and was sent packing by Korean combo of Kyung Eun Jung and Ha Na Kim 17-21 14-21 in just 26 minutes in the women's doubles.
It was also curtains for Rupesh Kumar and Sanave Thomas, who lost 17-21 16-21 to Hiroyuki Endo and Kenichi Hayakawa of Japan in 36 minutes.
Young qualifier Arundhati Pantawane also suffered defeat in the first round of the main draw, going down to Chinese Taipei's Tzu Ying Tai 16-21 13-21 in another women's singles match that last just 26 minutes.
Saina was the star performer for India once again as the fourth seed Saina, who had beaten Lan in the first round of Thailand grand Prix Gold last week, took little time to wrap up the first game after breaking off at 10-10.
However, the 24-year-old Chinese, who had won the World Championship in Hyderabad in 2009, got her act together and bounced back in the second game to draw level at 1-1.
In the decider, Saina opened up a 11-6 lead and held her fort as Lan crushed out of her second successive tournament at the Sinagapore indoor stadium.
