Maddon was thrown out in the seventh after the umpires likely blew a reversal call. Upton was ejected two innings later after he struck out for the fourth straight time.
"I just kind of lost it," Upton said. "I'm a pretty laid back guy, I think. Obviously, you could tell I didn't like the call. It is what it is. It's done with now."
Lind connected in the first inning and finished with four hits. He has five homers and 16 RBIs in his last 12 games.
Morrow (1-1) allowed one run and five hits in 6 1-3 innings. He struck out seven and walked four. Frank Francisco yielded Sam Fuld's RBI single in the ninth before finishing for his first save.
Blue Jays manager John Farrell was thrown out by plate umpire Chad Fairchild during a pitching change during the seventh.
Maddon was tossed by Joe West after the umpires got together and reversed West's safe call on a tag play by first baseman Lind on Fuld, completing an inning-ending double play. Lind was pulled off the bag by Edwin Encarnacion's throw after the third baseman recorded a forceout.
"I have a hard time with that call being changed from that distance," Maddon said. "If there's any particular play that screams for instant replay, it's that one. I just don't understand how you can make that call from that distance. I don't believe you can see it properly. If you're going to start changing calls from that distance, include instant replay. Then I wouldn't say a word."
West said he had the worst angle on the play, and consulted with the other crew members, including second base umpire Angel Hernandez.
"All I asked Angel was did he tag him, and Angel told me I thought you had him safe for being on the bag," West said. "I didn't heed that warning. I made the judgment based on what I had at first base. So it appears that we may have erred, but we did everything protocol right by the book."
Upton was ejected by Fairchild after striking out leading off the ninth. Upton slammed his bat and helmet to the ground, and had to be restrained by third base coach Tom Foley. Upton also threw several other items, including his arm guards, toward the plate area while heading toward the dugout.
"I actually had the privilege of watching it on television at that point, and those were pretty egregious calls, so I can understand why he was so upset," Maddon said. "I really believe that that particular AB should be reviewed by the umpiring higher-ups as opposed to it being all over B.J. Upton right now."
Tampa Bay starter Jeff Niemann (1-4) left after four innings with back tightness. The right-hander gave up three runs and six hits during a 62-pitch outing.
Since returning from a strained right shoulder last August, Niemann has allowed 56 earned runs over 63 2-3 innings in 13 starts.
Upton struck out in all three at-bats against Morrow. He has one hit in 13 at-bats — including nine strikeouts — overall against the Blue Jays starter.
Upton hit a two-run homer in the ninth inning of the Rays' 3-2 win over Toronto on Tuesday night.
Fuld's two-out single in the ninth got the Rays within one, but Francisco got Ben Zobrist to ground out with runners on the corners to end the game.
NOTES: The Rays will wear Navy SEAL Team 6 T-shirts as the theme for a road trip that starts Friday. The team wants to honor the naval unit that killed Osama bin Laden. "Tribute to their teamwork that enabled them to carry out their mission," Maddon said. "It's really picked everybody up. Everybody's got that good feeling about themselves right now." ... Blue Jays LHP Ricky Romero was scratched from his scheduled start Thursday against the Rays due to a mild left oblique strain.