Archer, who struggled in his season debut last Saturday in Cleveland, retired the final seven Orioles he faced and 13 of the last 14 to claim his second big league win in a pitchers' duel with Jason Hammel. Archer walked two and struck out two.
"This kid is a different cat," said Maddon. "He's really bright. He analyzes everything. He gets it. He's learned how to breathe out there. Sometimes, the bright kids get in their own way. But he doesn't overanalyze things. This validates that he can do this. He was spectacular."
"It was good to see my work coming to fruition," said Archer. "I've never said that word before. "I felt I was in control the whole time, honestly. I was able to stay within myself and execute pitches. It was one of those special nights that you try to tap into every game. Every pitch, I was telling myself what I wanted to do."
Hammel, the former Ray who leads the Orioles with seven wins, held Tampa Bay to three hits and had retired eight in a row until James Loney lined a single to center leading off the seventh inning.
Jennings then lofted the next pitch over the center-field fence for his sixth home run of the season, putting the Rays on top, 2-1.
"Not many balls go out there," Maddon said. "That ball was gone."
But Jennings, who was batting .248 coming into the game and was hitless in his first two at-bats, admitted he thought about bunting as he walked up to the plate.
"I'm glad I didn't," Jennings said, smiling. "I haven't been hitting the ball well. I was going to give myself one pitch. If that didn't work, I'd try something else."
Joel Peralta and Fernando Rodney worked the final two innings to secure the victory.
"You can never go wrong when you have the best setup man and the best closer in the the game coming in after you," Archer said.
The Orioles were understandably impressed by Archer's performance.
"His defense made some really nice plays and the kid is good," said center fielder Adam Jones, who was hitless in four trips. "He's got plus stuff. Everything he throws is plus. And it's going to be exciting to see his maturation over basically this year and the rest of his career, because he's one special talent.
"He's a product of their pitching. You've just got to see how [David] Price, [Jeremy] Hellickson and the rest of their pitchers teach them how to basically learn more at the big league level. I think that kid's got a very, very bright future."
After dropping two out of three to the Tigers in Detroit, Archer's gem was just what the Rays needed.
"We can only make up ground if we pitch well," said Maddon, whose team moved within half a game of the Orioles in the AL East standings. "We're not going to out-hit teams night after night. We need to pitch like that all the time."
The Orioles took a 1-0 lead in the third when Chris Dickerson and Nate McLouth walked and Manny Machado, who came into the game batting .320, singled to center for the first hit off Archer.
Friday's game was the first of 10 in a row at home for the Rays. Twenty-six of their next 36 games, leading up to the All-Star break, will be at Tropicana Field.
"We get to stay home for a while," Maddon said. "It feels like it's been one big road trip. It feels like it's been forever on the road."