In his third meet since returning from nearly two years out of the sport, the 28-year-old Phelps competed in multiple finals in the same session for the first time in his return to competitive swimming.
The most decorated Olympian of all time 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 second fastest by an American this year, behind Ryan Lochte.
Earlier, Phelps clocked 48.80 seconds in the 100 freestyle, beaten easily by Olympic champion Adrian, who touched the wall in 48.17.
Still, Phelps was happier with his freestyle result than with his fly.
He and coach Bob Bowman "are both kind of annoyed about going 52.1," Phelps said in a postrace interview 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 200 freestyle Saturday and the 200 individual medley 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."