The Spaniard's 68 came when the second round finally was completed after more than 24 hours of weather delays pushed its start back to Saturday.
Round 3 was suspended by darkness.
Swenson's 3-under 69 left both golfers with totals of 10-under 134 through 36 holes, one stroke better than Northern Ireland's Graeme McDowell (65) and England's Oliver Wilson (68).
"I stayed pretty patient," said Garcia, the winner at the Castello Masters two weeks ago. "It could have been different if I had made a couple of birdies earlier on."
"I had a great first round, then there was a long wait to get out there again," Stenson said.
Defending champion Phil Mickelson is within five shots of the leaders.
The event, being played at the Sheshan International Golf Club in Shanghai, marks the start of the tour's 2009 season.
Notable deaths of 2014 [PHOTOS]