He must win on Sunday to avoid missing out on a trip to Augusta for the first time since 1999, and he certainly got off to an encouraging start. He is one of 46 players in the field - his playing partners Ryo Ishikawa and Nicolas Colsaerts are two more - who need to win the title to be in the Masters field.
The 42-year-old Dubliner began on the 10th and holed from eight feet for an opening birdie, before picking up another shot on the par-5 13th. He dropped a shot on the next after failing to get up and down from a greenside bunker but quickly made amends with birdies on the 17th and 18th to reach the turn in 33.
A three-putt bogey on the third halted the former Ryder Cup man's momentum, but birdies on the fourth and sixth had him high on the leaderboard before a disappointing bogey on the ninth, his final hole.
"While I know it is my last chance to get into the Masters, I am not trying to do anything different; it's not as if I have a secret for good golf to keep for a week like this," he said. "A three-under-par start is okay but what I am ruing is that it could have been easily six or seven under. I haven't done any damage, but it's not where I feel I should have been."
At three under par, Harrington, whose last victory on a major tour was his 2008 US PGA Championship success, was three shots behind the early clubhouse leaders, Keegan Bradley and Matt Kuchar.
Bradley, who won the US PGA in 2011, carded six birdies in a flawless 66 that was matched by Kuchar in the group behind, the world No.11 missing from seven feet for birdie on his final hole to take the outright lead. Bradley's playing partners, Webb Simpson and Phil Mickelson, were also off to a good start, the pair returning rounds of 68 to join South African Ernie Els on four under par.
Mickelson, the Scottish Open and Open champion, had been a doubt for the event with a pulled muscle which forced him out of the Valero Texas Open last week, but the left-hander showed no ill effects as he carded four birdies and no bogeys.
"I feel a lot better now and the good thing is that I travel with a light therapy machine and I was working with it straight away on Saturday; that made a world of difference as far as expediting the healing process," he said.
"Coming to Houston, I feel like for me to have a realistic chance or as best a chance as possible at the Masters, I have got to play this week and get in a better frame of mind."
Els looked set to finish five under but dropped his only shot of the day on the 18th after twice finding sand.
Sweden's Henrik Stenson, who can replace the injured Tiger Woods as world No.1 with a victory in Houston, was five off the lead after a one-under-par 71.