American Perez, who moved to a cross-handed putting method two months ago, finished in style with birdies at the final three holes for a four-under 68 at the TPC San Antonio.
New Zealander Lee also plundered the closing stretch with four birdies in the final five holes to join Perez.
US PGA Tour rookie Andrew Loupe was also four under after 11 holes when play was halted by darkness.
Loupe was among 45 players who did not complete the round due to morning fog that delayed the start of play until 10am.
Perez, 38, whose sole US Tour win came in 2009, went cross-handed at the San Diego tour stop in January and promptly finished tied second that week.
"I want to putt conventional, but I don't putt well doing that," he told Golf Channel. "So I went back to cross-handed and started to putt well. I got some old feelings back that I had when I won, and I've just taken it from there."
South Korean-born Lee also changed his putting grip recently, going to the "claw" grip, so-called because the player rests his bottom hand lightly on the club and takes most of the wrist action out of the stroke.
"I was hitting it really good but I wasn't making that many putts early in the round but at the end I was making quite a lot of putts," said Lee, whose runner-up finish at the Puerto Rico Open three weeks ago did wonders for his confidence.
Three-times Masters champion Mickelson, meanwhile, hit only nine greens in regulation to fall nine strokes from the lead.
He also struggled on the greens, running up 32 putts and missing several short attempts, including one from barely two feet for a double-bogey at his final hole.
Mickelson will need a sizzling second round merely to make the halfway cut as he works towards Augusta.
While some players, notably Tiger Woods and Adam Scott, generally prefer to take time off before the majors and prepare at home, Mickelson likes to play his way in.
He is making his first appearance at the Texas Open in more than two decades, and is also planning to contest next week's Houston Open.
Four-times Major winner Ernie Els temporarily joined Mickelson at five over, before clawing back three late birdies for a 74.
The Texas Open, which dates to 1922, is the oldest US Tour event held in the same city every year.
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