The 63-year old Fleisher, making his third start of the year, had seven birdies and a bogey. He won the event in 2000 and 2003.
Fleisher, playing a limited schedule of 10 or 11 events, tied for 45th and 37th the previous two years.
Allen overcame a double bogey and bogey. He has finished second or third three times in five events this season.
Lu had consecutive birdies on 14 and 15, but three-putted three holes.
Gary Hallberg started his round with four consecutive birdies, but ended up at 69.
Langer, the 2010 winner, missed last year's event because of a thumb injury.
Cochran had a cortisone shot for a sore right wrist before the tournament and rebounded after bogeys on his second and third holes.
Kirk Triplett finished at 68 in his first Champions Tour round.
Tom Watson, playing with right arm and hand discomfort, had a 77.
Nick Price dropped out because of an injured left elbow, which has been hurting for the past three to four weeks. He played seven holes before leaving the course.
Tommy Armour III also withdrew after one hole due to a shoulder injury.
Louisville basketball coach Rick Pitino, a couple weeks removed from an unlikely trip to college basketball's Final Four, was among the amateurs playing.