Malnati, who fired a first-round 69, nabbed three birdies and an eagle in a confident trip around the course in southern Texas.
Countryman and overnight leader Talor Gooch made it through 14 holes and was one stroke off the lead when play was called due to darkness.
Austrian Sepp Straka and Americans Nick Watney and Lanto Griffin were tied for third.
Malnati, 32, who has missed the cut in his last two tournaments, said he was grateful to get out early.
"I got to play the first five holes in perfect conditions and really took advantage of it," said Malnati, whose wife is due to have their first child in the coming weeks.
"I then came back out and was able to keep the momentum going. To make no bogeys in the conditions we played is really more than I could have ever hoped for.
"I played the last 13 holes wishing I had hand-warmers. The wind was certainly a two or three club wind."