John Cook, a two-time winner of the Bob Hope, finished one shot off the lead at eight-under-par 64 along with Chris DiMarco.
Tway played the back nine of the Palmer Course at PGA West, one of four courses on rotation this week, and jumped out of the gate with an eagle at the par-5 11th after his second shot landed five feet from the cup.
Tway added a birdie at the 12th and another at the 18th for the first of three consecutive birdies around the turn.
'I got off to a good start,' said Tway. 'I was very pleased with how I hit the ball on the back side.'
The 1986 PGA champion, who is looking for his first win since 1995, drained a 20-foot putt for birdie at the fourth and reached 8-under with a birdie at the par-5 sixth. Tway then birdied the par-4 eighth to take the early lead.
'I was very pleased,' said Tway. 'I've always enjoyed coming to this tournament. This year, the weather is phenomenal. You are going to see some very, very low scores. I'm just pleased to get off to a good start.'
Ames also played the Palmer Course and he did it flawlessly. He collected four birdies on the front side and picked up two straight birdies starting at the par-4 10th. Ames dropped an 8-iron inside 18 feet for birdie at the 15th and drained a 35-footer at the very next hole.
The Trinidad native then two-putted for birdie at the par-5 18th for his share of first.
'Everybody comes here thinking it's going to be a putting competition, which basically it ends up being,' said Ames. 'You know you're going to have to make putts.'
DiMarco opened with four consecutive birdies on the back side at Bermuda Dunes and added a birdie at the par-5 18th to make the turn at minus-5. DiMarco continued his fine play on the inward half with three birdies to finish one off the lead.
'It really doesn't matter which course you're playing. If you're not driving the ball really straight and not putting yourself in position to make birdies, any course is going to play though,' said DiMarco. 'You just have to stay patient out there.'
David Duval made his 2003 debut in impressive fashion with a 7-under 65 on the Classic Course at Indian Wells Country Club. Duval was joined by Robert Gamez, Frank Lickliter, Shaun Micheel, Rod Pampling, Matt Gogel and Dave Stockton, Jr. in a tie for fifth.
'You would think I would play really well sleeping in my own bed and knowing the golf course as well as anybody,' said Stockton, who lives nearby. 'I think I just put too much pressure of myself in the past. I told myself this week that I was going to be focused by going out and having fun. That's what I did today.'
Esteban Toledo had six birdies and no bogeys at La Quinta Country Club to finish one shot further back at 6-under-par 66 alongside Mark Calcavecchia, Jonathan Kaye, Justin Leonard, Doug Barron, John Huston and Dan Forsman.
Defending champion Phil Mickelson teed off on the back side at Bermuda Dunes and birdied three of his first six holes but found trouble with a bogey at the 17th. Mickelson recovered with a birdie at the par-4 third but faltered with a bogey at the seventh for a round of 70.