In his third meet since taking nearly two years out of the sport, the 28-year-old Phelps competed in multiple finals in the same session for the first time on his return to competitive swimming.
The most decorated Olympian of all-time (22 medals, 18 gold) matched Shields with a time of 52.11 seconds to share top spot in the butterfly, finishing the faster of the two but unable to edge his way in front.
The pair's time was the joint-second fastest by an American this year behind Ryan Lochte.
Earlier, Phelps clocked 48.80 seconds in the 100m freestyle, beaten easily by Olympic champion Adrian, who touched the wall in 48.17.
Phelps was still happier with the freestyle result over his fly, given how he and coach Bob Bowman had targeted more improvement.
"Bob and I are both kind of annoyed about going 52.1," Phelps said in a post-race interview that was posted on Swimming World magazine's website.
"It's the third time we've done it this year. We'd like to make a bigger breakthrough.
"I wanted to go under 49 and I wanted to go under 52... I got half of that."
Phelps is scheduled to swim the 200m freestyle on Saturday and the 200m individual medley on Sunday.
"We'll see how I'm going to feel tomorrow morning," he said after getting through his first double finals session. "I think it was a pretty good day."
The women's headliner of the meet, Missy Franklin, finished second in the 100m freestyle behind Simone Manuel.
(Reporting by Ben Everill in Los Angeles; Editing by John O'Brien/Sudipto Ganguly)
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