Crawford hit Lohse's first pitch over the center-field fence and later homered off him again, leading Clayton Kershaw and the Los Angeles Dodgers over the Milwaukee Brewers 2-0 Sunday.
"I came into it knowing Crawford's an early swinger—especially against a guy like me, who's trying to pour strikes in there," Lohse said. "It's just one of those things where he caught me on the first pitch right over the plate. You can't do too much about it. I mean, I'm not going to throw a first-pitch curveball."
It was the fourth time Lohse had given up a home run to his first batter in 336 career starts, and the first one that came on his very first pitch.
The other leadoff homers Lohse yielded were by Jose Valentin (2001), Chuck Knoblauch (2002) and Jayson Werth (2011).
"The past week, guys have been getting ahead of me with the first pitch right down the middle. So I just picked today to be aggressive with the first pitch," Crawford said. "This is a tough ballpark to hit home runs in, but they say the ball flies better here in the daytime. So I caught a break today."
Crawford's second homer came on an 0-2 count in the fifth inning and landed in the right-field pavilion. It was his sixth multihomer game in the majors and first since July 8, 2010, for Tampa Bay.
Lohse (1-2) gave up five hits and no walks while striking out four in seven innings.
Milwaukee signed the right-hander to a three-year, $33 million contract as a free agent on March 25.
"He's a huge addition to our pitching staff," Brewers manager Ron Roenicke said. "That's not a knock on our young guys, but having him on the staff along with Yo (Yovani Gallardo), I think that makes us a very good team."
Kershaw retired 18 consecutive batters and struck out 12 in eight dominant innings.
Kershaw (3-2) scattered four hits and didn't walk a batter while lowering his ERA to 1.73. The 2011 Cy Young Award winner, who led the NL in ERA in each of the previous two seasons, hasn't allowed more than three earned runs in any of his last 18 starts—the longest active streak in the majors.
The All-Star lefty stranded runners in scoring position in each of the first two innings, retiring Jonathan Lucroy on a double-play grounder in the first and striking out Martin Maldonado to end the second.
Kershaw gave up a leadoff double in the eighth to Carlos Gomez, who tried to advance on a broken-bat comebacker to Kershaw and was tagged out by third baseman Juan Uribe in a rundown.
"You've got a bat that's exploding, you've got a chopper back to the mound, and sometimes you're not going to read it well," Roenicke said. "But at that part of the game, we needed two runs. So whether he's on second base or Maldonado's on first, we've still got to drive in two runs."
Brandon League pitched a perfect ninth inning for his eighth save in nine chances.
NOTES: Lohse reached the 2,000-inning mark for his 13-year career when he retired Kershaw on a grounder to shortstop to end the second. ... Lohse, coming off a 7-1 win last Monday at San Diego, hasn't won consecutive road starts since last April against Cincinnati and Pittsburgh. ... Gallardo will pitch the opener of a three-game set against Pittsburgh on Monday at Miller Park. He is 6-0 with a 2.18 ERA in his last seven starts overall against the Pirates.