The former world number one had three birdies but dropped four shots on the back nine to finish up six-over, the same score as Shane Lowry.
"I'm very pleased. I'm very excited about it", Woods said as darkness settled Friday over Riviera Country Club.
"For her only child to go through the struggles was a little rough on her", Woods said, "so she's very proud of me getting back out there".
Northern Ireland's McDowell shot a five-under 66, while Cantlay posted a 69.
Despite blowing an opportunity at birdie on the short par-5 first hole, the 14-time major victor picked up a birdie at the par-4 third hole.
Former US Open victor McDowell has just one top-10 finish worldwide in the past 18 months.
Three of the past four tournaments at Riviera have been won by Bubba Watson (twice), and previous year by Dustin Johnson.
He said his game for the past several months had been much better than those results indicated.
Missing the cut at Riviera will offer him extra time to recover from soreness and to prepare for the Honda Classic, which is near his current residence in South Florida.
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"I think it would be a great sign if I do play", he said on Tuesday.
But imagine the chaos the well-lubed fans surrounding the infamous par-3 16th at TPC Scottsdale during the Phoenix Open cause, and you get a snapshot of what Woods faces on each and every shot.
Like three weeks ago at Torrey Pines, when an idiot yelling "Get in the hole" while Woods was putting likely produced a missed birdie putt.
This week the missed fairways were joined by plenty of missed greens and, on Friday, missed putts.
"I was at one-under early, first hole, and all of a sudden I went double bogey-bogey and I was like, 'Oh, man, here we go, '" Woods said.
"He's very close. He is very close", McIlroy said a second time. "That was frustrating, because I knew where to hit it and I wasn't able to hit it there".
But it's tiring. I need a couple of Advil. He did not mention trouble with his back, and he committed to playing in the Honda Classic in the coming week.
"I haven't played golf in years", he continued.
Bubba Watson kept himself within a few strokes of the lead Friday with a one-under 70, which puts him at four under for the tournament.
Throughout this entire process, which began last April when he had fusion surgery on his lower back, Woods has talked of benchmarks and protocols. They were both in a group of 10 sharing 15th place on two-under.