Woodland and former Masters champion Reed both shot six-under par 66 at wind-whipped Albany Golf Club -- displaying the kind of solid golf US Presidents Cup playing captain Woods was hoping to see from the pair when he selected them for this month's matchplay showdown with Ernie Els' International squad.
Woods himself had his struggles, improving from two-over through 10 holes to reach three-under before closing with a bogey and double-bogey in an even-par 72.
Woods made a run up the leaderboard with birdies at 11, 13 and 14 followed by an eagle at 15 -- where his chip from off the green took two bounces and rolled into the hole.
"Got it going on the back nine just a little bit, got myself kind of right there in the mix and then bad shots on 17 and 18," Woods said.
Woods wasn't the only player to run into trouble at Albany's closing hole -- where Patrick Cantlay finished with a quadruple bogey and Jordan Spieth a triple bogey.
Despite the disappointing finish, Woods wasn't discouraged about his game.
"I didn't putt well today," he said. "My short game was great, drilled it really well, just hit a couple of poor iron shots that cost me a few shots."
Woodland said keeping it in the fairway was the key to his round, which included eight birdies and two bogeys.
"The wind was tricky," he said. "Fortunately I drove the ball really well, gave myself a lot of looks from the fairway which you've got to do.
"Obviously when you have a lot of birdies you see putts go in -- so all in all a good day."
"Nice to get the game trending in the right direction," he added. "Obviously next week is a big week -- but so is this week."
- Patience key for Reed -
Reed, who reeled off four straight birdies from the 13th through the 16th to join Woodland on six-under, said patience was key in the challenging conditions.
"When this wind's blowing like this, you're going to hit some great putts and great shots that are not going to turn out very well," he said. "And you're going to hit some bad ones that go your way."
Woods hosts this 18-man event for the benefit of his charitable foundation. It's not an official US PGA Tour tournament, but offers world ranking points.
The 15-time major champion is also looking ahead to next week's Presidents Cup at Royal Melbourne, saying he's spending considerable time this week prepping himself and his players.
"We have some things we need to run through with the guys, some ideas," Woods said. "We want to have a clear picture of what we want to do down there because obviously once we get down there things roll pretty quickly."