Tiger Woods found himself six shots behind after the opening round at the Muirfield Village Golf Club and Rory McIlroy fired the highest first-round score, a 76, that he has ever posted in a tournament held in the United States.
Schwartzel suffered the double bogey at the par-3 eighth, his 17th of the day, but rebounded to birdie the ninth hole and seize a one-shot lead over Scott Piercy.
Josh Teater, Kyle Stanley, Charlie Wi and Russell Henley all turned in a 67 to share third place. Henley is one of this year's PGA Tour winners, having captured the Sony Open in what was his debut as a tour member.
Woods, the only multiple winner on the circuit this year with four victories, settled for a 71 in a round that included four bogeys. He has won this tournament four times and is the defending champion.
McIlroy played a 10-hole stretch in 7-over and eventually finished with a 76. He was in front of only six players in the 120-man field.
Schwartzel won the 2011 Masters, which has been his only victory on the PGA Tour. He has nine other international wins, including this year's Alfred Dunhill Championship on the European Tour.