After six straight pars, McIlroy carded his double bogey on the 16th - his seventh hole of the day having started on the 10th - after having to play left handed from under a tree and made the turn two-over.
Reed didn't make a par over the last six holes, with four birdies and two bogeys.
Englishman Rose turned in 33 to open up a one-shot lead at Sheshan International Golf Club.
His double bogey on the 17th hole sent him from a two-shot lead to a one-shot deficit, and then he compounded it with another mistake on the 18th.
"That's about as bad a break as I have ever had".
"I'm looking forward to tomorrow", said Finau after closing his round of... Americans now have won 41 of the 69 events since the World Golf Championships series began in 1999. "I didn't have an incredible Asian Swing up until this point, so I think that flight home will be a little bit more special".
"It was pumping out there", Reed said of the swirling winds.
"It's a lot to take in honestly", Schauffele said.
The American told www.europeantour.com: "It felt really good because if you can go out and shoot rounds like that in these kind of conditions, you know you're going to have confidence when the wind dies down and there are flawless conditions out there".
Reed had a putt for birdie on each of the holes during the opening round of the event, which he ended without a bogey to his name.
After slicing his drive into the water, Reed faced a hard third shot from a downhill lie and with about 220 yards to the green.
"After hitting the tee shot in the water, you're always happy to be able to walk off with par", he said.
The tournament, dubbed "Asia's major", annually gathers a premier crop of players and carries a winner's purse of $1.8 million.
Tenth-ranked Jason Day of Australia totaled 71 and is tied for 24th, top-ranked Brooks Koepka and fifth-ranked Rory McIlroy of Northern Ireland are in a tie for 27th at 72, eighth-ranked Jon Rahm of Spain is tied for 41st at 73, second-ranked Dustin Johnson shot 74 and is tied for 49th, while sixth-ranked Francesco Molinari of Italy struggled to a 76 and is tied for 68th.
Four-time major victor Rory McIlroy followed his opening round even-par 72 with a 77 to sit well off the pace.