Bettencourt lost his tour card last year following a poor season and this is only his third appearance on the circuit in 2013.
He shot a 5-under-par 67 at the TPC-San Antonio Oaks Course on a chilly, windy day and wound up tied for the top spot when Peter Tomasulo, playing in the final group of the day, birdied the final two holes.
Tomasulo put together a rare bogey-free round for his 67.
Harrington captured three major titles in the span of 14 months, the last of those being the 2008 PGA Championship, but he has not won in the United States since then.
Jordan Spieth, who at age 19 has earned at least temporary tour membership by collecting more than $500,000 in the first three months of the year, was 4-under with two holes to play before suffering a triple-bogey. He wound up with a 1-under 71.
Rory McIlroy, hoping to find some of his former magic before next week's Masters Tournament, settled for a 72. McIlroy, recently replaced by Tiger Woods as the world's top-ranked player, had three bogeys in a row during the middle portion of his round.