Former U.S. Open champion Lucas Glover and Kevin Tway each shot 7-under 65 in the morning.
The start of the tournament was delayed by two hours because of torrential rain.
Overall, Ryder Cup star Poulter has responded superbly in Houston to the disappointment of narrowly missing out on an automatic place at the Masters, having found himself 51st in this week's world rankings, with the top 50 players receiving an invite to the year's first major.
And he may get it in Texas where he got off the ideal start, hitting a wedge to five feet at the 10th before making the birdie putt to get into the red straight away.
"I didn't make a birdie on the back nine and that's disappointing", Mickelson said.
Lindberg, out in the last group of the day off the 10th tee, stole the limelight, gathering seven birdies, including a chip-in at her 15th hole, the par-four sixth.
"I really just had the two holes that obviously cost me a few shots there and kept me from being in a real good spot for tomorrow", Fowler told Golf Channel. Both played for the University of Texas, but not together.
It was also a good day for three-time Major victor Jordan Spieth as he seeks confidence ahead of the Masters. My goal is to try to get in contention for the weekend. The world No 5 once again highlighted his rude form going into Augusta, where he intends to go one better than past year.
Madison resident Steve Stricker needed to win the tournament to earn a berth in next week's Masters, but missed the cut - the line was 3-under - by a stroke. He ran off five consecutive birdies through the middle of his round and added two more late in his round for his lowest score of the year.
"I got off to a nice start as you can see with four birdies through the first six, but it would have been nice to get a couple better looks through the rest of the round and finish off a little bit better", Fowler said. "I've played some really good golf like this". "I don't know why or how".
After an opening 67, Stricker faltered to a second-round 75 that included five bogeys and left him 2-under 142.
Ian Poulter is on the verge of picking the ideal time to produce a first career strokeplay victory in the United States.