McIlroy (6) and Spieth (4), joined Dustin Johnson (1), Jon Rahm (3), Hideki Matsuyama (5), Jason Day, (8) Tommy Fleetwood (9) and Paul Casey (10) as the other top 10 seeds making an early exit.
Only world number two Justin Thomas, seeded second, and Masters champion Sergio Garcia (7) made it through the cut throat group stage.
McIlroy had to beat Harman on the final day of round-robin play to have a chance of qualifying for the weekend, but it was all one-way traffic in Harman's favour.
Despite being outdriven by 60 yards at times, 18th seed Harman proved steadier, losing only one hole.
"Rory did not play his best golf today but I played extremely well," two-times PGA Tour winner Harman told Golf Channel.
"I'm proud of the way I came out. Rory is an intimidating guy. He hits it a mile. I had this one (match) circled this week and I'm glad I came out and performed pretty well."
Harman was the first player in the 64-man field to advance to the knockout stage.
Spieth later made a demoralising start against Reed, with awful drives at the first two holes leaving the British Open champion two down.
Spieth and 19th seed Reed came into the game after two straight wins, with the winner guaranteed a place in the next round. The winners of each of the 16 four-man groups qualified for the weekend.
Seven of the 16 qualifiers advanced with perfect 3-0-0 records -- including Thomas, who was in sizzling form in a 7&5 win over Italian Francesco Molinari.
"Today I'd be really excited to see how low I could go. I could post a serious number," said Thomas.
Garcia also won his group with a perfect record after beating American Xander Schauffele 3&1.
Top seed Johnson, last year's champion, had already been eliminated before Friday's play and posted his third straight loss, going down 4&3 against Kevin Kisner.
Bernd Wiesberger drained a 20-foot putt at the final hole to halve his match with Canadian Adam Hadwin, a result that allowed Kisner to win the group.
The round-of-16 matches will be played Saturday morning, followed by the quarter-finals in the afternoon.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Christian Radnedge/Peter Rutherford)
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