Bay played left field and went 1-for-3 with a double, walk and run scored. He struck out twice.
He missed the past two games -- both Mets losses -- to be with his wife, Kristen, for the birth of their third child, a son named Garrett.
"My mother-in-law got in town so she spent the night at the hospital last night, so I got a decent night's sleep," said Bay, who walked into the Mets' clubhouse just after 10:30 a.m. ET Thursday. "And then [this morning I] had to run to the hospital. Wife and baby got discharged, drove home, dropped them off, probably got there at about 10 o'clock, and then just drove straight here.
"I could use a little more sleep, but anybody could."
Major League Baseball instituted a new paternity leave list this season, allowing players to step away for 24 to 72 hours and permitting teams to add another player to the roster in the interim.
"It's classy, I guess -- you afford the team that luxury and make it so that the player doesn't have to worry about leaving somebody shorthanded," Bay said. "I think that that was a nice luxury to have that."
Lucas Duda, who was recalled from Triple-A Buffalo in Bay's stead, has been sent back to Buffalo. Duda, who hit just .118 (2-for-17) in his previous stint in the majors this season, went 0-for-3 the past two days, striking out looking twice and fouling out to left.
Kieran Darcy is a staff writer for ESPNNewYork.com.