The 14-time major champion had bogeys on seven of his first 12 holes before closing with birdies on three of his last six holes.
Woods' round was characterized by several sloppy mistakes around the greens. Yet he drove the ball accurately, hitting nine out of 14 fairways. He also hit 10 of 18 greens.
"The score is not really indicative of how I played," he said. "I had four up-and-downs right there on 15 through 18. I had an easy pick on 2, don't get that up-and-down and a wedge in my hand on 3 and I jerk it in the bunker."
Greg Chalmers finished with three straight birdies for a 66 and has a one-shot lead over Ricky Barnes and Freddie Jacobson.
Defending champion Bill Haas, Patrick Reed, U.S. Open runner-up Erik Compton and Tyrone Van Aswegen shot 68. Compton birdied his last four holes.
"I didn't think it was easy at all," Chalmers said. "I played really well, and I think anybody who plays really well can shoot a low score. You just have to be coming out of the fairway, and I didn't that the majority of the time today."
Only 26 players in the 120-man field broke par.
Only once in his career has Woods shot as high as 74 and gone on to win the tournament. It happened in the 2005 Masters, when he was tied for 33rd after the first round after shooting 74.
Woods, who last played in a PGA Tour event in early March, said the most difficult aspect of Thursday's round was getting into the rhythm of playing competitively.
"You play with your buddies all day for cash and stuff, but it's just not the same," he said. "It's not the same as tournament golf, different level. Adrenaline is rushing, and I hit the ball further out here than I do at home.
"I was trying to get the numbers and the feel. That didn't start happening until midway through my front nine."
Woods, who said his back felt great, was pleased to be back in competition.
"I unfortunately have been in my career on the sidelines enough," he said. "So it's always fun to come back out here and play against these guys, the best players in the world, and to get out here and see what I can do."
On Friday, Woods will start his second round at 1:12 p.m. ET with Jason Day and Jordan Spieth.
"It was a great group," Woods said of his pairing with Day (73) and Spieth (74). "Unfortunately, we didn't see a lot of each other on the front nine. We were all kind of looking to break 80. It was a bit of a fight for all of us, but we hung in there."
The Associated Press contributed to this report.
Tiger Struggles In Return
In his first tournament since March, Tiger Woods shot a three-over in the first round of the Quicken Loans National.