The Rays had led 6-1, but the Cubs scored two with two outs in the fifth, then put their first two hitters on base in the sixth.
Archer didn't give in. He dug in.
Down went Addison Russell on three pitches, taking a 97-mph fastball on the outside corner after Archer got ahead with two sliders. Tommy La Stella worked Archer for seven pitches but struck out on a 2-2 slider that broke inside at his knees.
Then Archer finished the job by throwing a 96-mph, 1-2 fastball past Jon Jay. The three straight strikeouts completed a 116-pitch effort for Archer, who would pick up the victory after Alex Colome survived a ninth-inning rally.
"I really like the way Arch battled through that sixth inning,'' manager Kevin Cash said. "First and second, nobody out, and nobody comes across to score. That was pretty telling, a big moment in his season for us.''
Or maybe a big moment for one of several contenders.
Archer, in his prime at age 28 and under team control through 2021, has become the Moby Dick of trade targets. He's the big fish every general manager dreams about, even if there is little chance he can be reeled in.
The cost to do so would likely surpass the asking price for the other controllable starters -- most notably, Marcus Stroman, Jose Quintana and Sonny Gray -- even though Archer has a losing career record (48-56). He led the Major Leagues with 19 losses a year ago but is bouncing back to his form in 2015, when he finished fifth in Cy Young voting.
When Archer went to the mound to face Colombia in Team USA's World Baseball Classic opener in early March, he seemed poised for a big season. But nothing has come easy for him as he compiled the 7-5 record and 3.95 ERA he'll take into his final start of the first half on Sunday, facing David Price and the Red Sox.
Too many times he's not gotten the big outs or his inherited runners have been allowed to score. He's holding opponents to a .243 opposing batting average but his BABIP is .328, which partially explains why his ERA is so much higher than his Fielding Independent Pitching metric (3.02).
"I think for the most part this whole season my stuff has been really good,'' Archer said. "I've been getting some mixed results but I've had a lot of games that were comparable to [the one against the Cubs]. Some of them, the [pitching] line was a little bit better; some of them it was a little bit worse. But [this] was just a normal day for me, honestly.''
That speaks loudly, given how sharp Archer's pitches were against the Cubs. His fastball averaged 96 mph, with 99 in the tank on occasion; his slider averaged 90.1 mph. He threw both for strikes, piling up 80 strikes on the afternoon (69 percent).
The strike total included 24 swinging strikes, matching a career high that dates to 2015. Swings at his trademark slider produced contact barely 70 percent of the time.
"I don't know how much better Arch's stuff can get,'' Cash said. "He was throwing 96 to 99 mph with 90-mph sliders. That's pretty good stuff.''
Archer had escaped the fifth inning by blowing away dangerous rookie Ian Happ in a three-pitch strikeout. He went slider-fastball to start the at-bat, then finished him with a harder slider than the first one. It started at the thighs and broke down to the ankles. Happ swung and missed, and Wilson Ramos blocked it.
"His stuff started to tick up there,'' Cash said. "The slider started getting below the zone. When he's doing that, my gosh.''
Joe Maddon would love to see the Cubs land Archer as a long-term piece of a rotation that could be missing Jake Arrieta in 2018, even if he can't say it. He was the Rays' manager when Archer made his debut in 2012.
"I didn't know what to expect [from Archer], honestly I didn't,'' Maddon said. "I saw him in camp. Great arm but didn't really have a good feel for command at the time. Fastball command wasn't there. … Then all of a sudden he started finding the plate, and that slider's electric.''
Both Maddon and Archer are big readers and free thinkers. That provided them common ground from the start.
"When you talked to the kid you [had to like him],'' Maddon said. "He and I connected on an intellectual level regarding books and stuff. He's really well-read. He's a lot smarter than I'll ever be. I've always enjoyed my conversations with him.''
Archer's smart enough not to spend too much time dwelling on possibilities beyond his next few starts and what he hopes will be the Rays' postseason push in August and September.
"I think rumors are just rumors,'' Archer said. "My main focus is winning a World Series with the team I'm on. I think we have a really good team. I think we can do something special here.''
The Rays have hovered around .500 all season, never more than four games above or three games below. They may be challenged to hang with the Red Sox (and maybe Yankees) but seem deep enough to factor in the American League Wild Card race.
That's what the front office was thinking when it acquired glove-first shortstop Adeiny Hechavarria from the Marlins in late June. No one appreciated that deal more than Archer.
"Look at championship caliber teams -- [at] catcher, shortstop, second base and center field, the defenders are elite,'' he said. "Look at the Cubs last year. Look at the Royals in past years. Up the middle, they have been elite. Making that move, it made us elite up the middle.''
Archer looks ready to be a difference-maker for a contender, most likely the one he's already on.