US seventh seed Will Zalatoris and Norwegian eighth seed Viktor Hovland were also among five top group seeds to fall on day one at Austin (Texas) Country Club.
Sixteen winners from four-man groups will advance to weekend knockout rounds.
Reigning Masters champion Scheffler, who won the Players Championship earlier this month, sank a 13-foot birdie putt at the 18th hole to edge US 54th seed Davis Riley 2&1.
"Fortunate to come away with a win," Scheffler said. "I'm going to remember that putt on the last hole and take that energy into tomorrow."
Scheffler, who never trailed, holed out from 52 feet for eagle to win the par-4 fifth hole and eagled from 24 feet to take the par-4 13th.
Riley missed a three-foot birdie putt at the par-5 16th that would have pulled him level but Scheffler missed a 3.5-foot putt at the par-3 17th to win the match.
"I got off to a really good start. Outside of that I didn't really play great," Scheffler said. "Fortunately I saw that putt go in on 18."
South Korean Tom Kim edged Sweden's Alex Noren 2&1 in Scheffler's group.
Spain's Rahm fell to US 49th seed Fowler 2&1. Rahm, a three-time PGA winner this year, missed a par putt from just inside five feet to drop the 15th. Fowler sank a seven-footer for par at 16 and halved 17 as well to win.
"Just had to stay patient and rely on iron play," Fowler said. "I just kept grinding and pushing forward."
It was Fowler's first appearance at the event since 2016 and Rahm's first opening-match loss in six starts.
Four-time major winner McIlroy beat American Scott Stallings 3&1 with a new putter and new driver.
"It was a good first outing for both those clubs," McIlroy said. "They performed pretty well."
The 2015 Match Play winner from Northern Ireland said the event helps prepare him for stroke-play challenges to come.
"There's a ton of golf left this season but to get a bit of match play in our lives is good, and to get under pressure," McIlroy said.
US 20th seed Keegan Bradley, 4-down after 13, won four of the last five holes, his six-foot birdie putt taking 18 to tie countryman Denny McCarthy in McIlroy's group.
Zalatoris dropped the last three holes to fall 3&2 to 56th-seeded compatriot Andrew Putnam.
US 59th seed Matt Kuchar, the 2013 Match Play champion, won 3&1 over Hovland. Kuchar, at 44 the oldest in the field, is one shy of Tiger Woods's event record 36 match wins.
SCOTT: 'SATISFYING' WIN
Aussie 33rd seed Adam Scott sank a 26-foot birdie putt at the 18th to grab his only lead in a 1-up victory over Irish 30th seed Seamus Power.
Scott, the 2013 Masters champion, last won a PGA title in 2020 at Riviera.
"I haven't won anything much in a long time," he said. "A win feels satisfying."
South Korean 16th seed Im Sung-jae beat US 58th seed Maverick McNealy 8&6, matching the most lopsided group win at Austin.
US 61st seed J.J. Spaun never trailed in upsetting England's 11th-seeded Matt Fitzpatrick 5&3. Spaun won four of the last five holes from the reigning US Open champion with three birdies and an eagle hole-out from 107 yards at the par-4 13th.
"I just slung it with the wind," Spaun said. "I could tell it was going to be pretty good, but then it got really good and then it just disappeared and the crowd went nuts."