Eger, the former PGA Tour and USGA executive who won the last of his two Champions Tour titles in 2005, had six birdies and two bogeys on the TPC Tampa Bay course.
"The score is great. But I wasn't happy with the way I have hit the ball," Eger said. "I hit some good irons, but I didn't hit a lot of good tee shots. It could have been better."
Tom Wargo opened with 68, and Jay Haas, Wayne Levi and John Harris shot 69s on the chilly day when temperatures dipped into the low-40s.
Mark O'Meara had 74 in his first Champions Tour round.
"There was probably a little bit more pressure on me since the last few years there really hasn't been that much pressure," O'Meara said.
SBS OPEN: In Kahuku, Hawaii, Morgan Pressel shot 4-under-par 68 for a share of the lead midway through the second round of the LPGA Tour's season-opening tournament.
Sherri Steinhauer (70) matched Pressel at 7-under 135 after the morning session.
Paula Creamer, who shared the first-round lead with Steinhauer and Paige Mackenzie, also was 7 under through the front nine.
JACOB'S CREEK OPEN: In Adelaide, Australia, Australian Craig Parry shot 8-under-par 64 for a share of the second-round lead.
Parry matched fellow Australian Brett Rumford (69) at 9-under-par 135 on the Kooyonga course in the event sanctioned by the Australasian and Nationwide tours.
INDONESIAN OPEN: In Jakarta, Indonesia, Andrew Tampion took the clubhouse lead after shooting 5-under-par 66 in the storm-interrupted second round.
Tampion, who became a pro in November, fired six birdies to lead by three strokes at the Damai Indah Golf and Country Club.
Suk Jong-yul carded 68 to share second place with Nam Young-woo, who fired 69 during his round.