World number one Tiger Woods of the U.S. plays from a bunker onto the 16th hole green on day one of the Accenture Match Play Championship at the Ritz-Carlton Golf Club at Dove Mountain course in Tucson, Arizona. (Mark Ralston/AFP/Getty Images)
Harrington, winner of three of the last six majors, lost by a hole to American Pat Perez and Spanish world number two Garcia went down by the same margin to South African Charl Schwartzel.
Top-seeded Woods, back in action after an eight-month absence due to knee injury, thrilled a huge gallery on a sun-baked day at Dove Mountain's Ritz-Carlton Golf Club by beating Australian Brendan Jones 3&2.
"I think my game is right there but I didn't give myself the chances today and I was not as sharp as I could have been," fourth-ranked Harrington told reporters after losing in the first round for a fourth time.
"I lost it on the fifth hole. I missed a putt there and made a terrible five from the middle of the fairway when he was in trouble.
"Everything after that was a bit of a struggle," added the Irishman who went one down after bogeying the first and never led in the match. "I had a few putts here and there but that was a momentum shift there."
Garcia survived a barrage of three consecutive birdies from the first by Schwartzel to go two up after 15 holes before losing a fluctuating encounter with a bogey at the last.
Defending champion Woods, making his hotly anticipated PGA Tour comeback, charged two up after a birdie-eagle start before wrapping up his win on the 16th green.
Getting rhythm
"I thought it would take me a little bit longer to get into the rhythm of the round but I came out as if I had it and it felt good," Woods said after piling up two eagles, three birdies and three bogeys.
"I hit a couple loose irons in the middle part of the round but, other than that, I really hit it pretty good all day."
Asked how his surgically reconstructed left knee had held up, the three-times champion replied: "I'm very pleased at how it felt all day.
"I thought that it would be more stiff on the 15th tee when I had to hit my shot after that long wait, but I felt fine."
World number three Phil Mickelson squeezed past Argentina's Angel Cabrera after 19 holes, fellow American Anthony Kim crushed Taiwan's Lin Wen-tang 7&5 and South African Ernie Els beat Dane Soren Hansen 4&2.
Britain's Oliver Wilson upset South Korean KJ Choi 3&1, American Zach Johnson won a high-quality contest with Britain's Graeme McDowell 3&1 and Japan's Shingo Katayama came from two down after 11 holes to beat South African Trevor Immelman 3&2.
In other matches, Colombia's Camilo Villegas thumped Australian Rod Pampling 7&6 and Britain's Lee Westwood beat Thailand's Prayad Marksaeng 2&1 with a flawless five-birdie display.
