Rizzo's solo homer in the fourth inning made him the first player in Yankees history with at least one RBI in each of his first six games with the club.
Rizzo became just the fourth player in the majors over the last 70 years to do it - Bobby Murcer drove in a run in his first seven games with the Chicago Cubs in 1977 and Jimmy Wynn (Dodgers, 1974) and Jim Spencer (Texas, 1973) did it six in a row, according to the Elias Sports Bureau.
''It's definitely special. It's something that you put on a Yankee uniform, a lot of kids out there dream of playing for the New York Yankees growing up and there's a lot kids out there right now that are dreaming,'' Rizzo said.
''To be able to come in at the trade deadline and just have success right away is something I'll never take for granted - these last few games, this start. To be No. 1 at anything for a Yankee is very special, is very humbling because of the history here and all the success here,'' he said.
Sent from the Cubs to the Yankees last Thursday, a day before the trade deadline, Rizzo hit his 17th home run of the season and third for the Yankees. He has six homers in his last 10 games overall.
LeMahieu had three hits and Giancarlo Stanton drove in three runs for the Yankees, who routed the Orioles 13-1 on Tuesday.
At 58-49 the Yankees matched their season high of nine games over .500, set May 23 when they were 28-19.
The New York offense has posted double-digit runs in consecutive games this season for the first time.
The trades for Rizzo and Joey Gallo have certainly evened out the lineup, according to Yankees manager Aaron Boone, who now hopes it will produce at a higher pace.
''I think it's the weight of our lineup. It's starting to pay some dividends,'' Boone said.
Jonathan Loaisiga (8-4) got two outs for the win. Yankees starter Jameson Taillon struck out 10 in 6 1/3 innings.
Ryan Mountcastle hit his 19th homer and a sacrifice fly to put Baltimore ahead 3-0 in the fourth.
Orioles starter Matt Harvey extended his scoreless-inning streak to over 21 innings before Rizzo homered.
Harvey, who had won his previous three starts, allowed two runs and three hits in four innings, but was pulled early after feeling discomfort in his left leg while fielding a grounder in the second inning.
''I think going forward in the outing I felt like I couldn't quite push off the rubber and stay in my mechanics the way I needed to, especially against a lineup like that,'' Harvey said.
It was 3-all when the Yankees scored five times in the seventh. Cole Sulser (3-2) walked the first two batters in the inning before he was pulled for Paul Fry.
LeMahieu then hit a hard grounder that went through Fry's legs and glanced off the glove of diving second baseman Ramon Urias for a single, scoring pinch-runner Jonathan Davis with the go-ahead run.
After Rizzo flied out, reliever Dillon Tate struck out Aaron Judge and walked Joey Gallo to load the bases. Stanton lofted a flyball to shallow right field that was out of the reach of Mountcastle, the first baseman, allowing all three runs to score to extend the lead 7-3.
Orioles: Baltimore purchased the contract of RHP Marcos Diplan from Triple-A Norfolk. . RHP Dusten Knight also had his contract purchased from Norfolk. He made his debut in the eighth inning and gave up two runs off three hits. . RHP Shaun Saunders and INF Domingo Leyba were designated for assignment.
Yankees: Davis, who was picked up on waivers from Toronto, was added to the roster. ... OF Greg Allen, who was brought on to the roster as a replacement player, was sent to Triple-A Scranton/Wilkes-Barre following the game.
TAKING HIS TIME
While the Yankees have two starting spots open this weekend, one of them will not be held for Luis Severino, who on Tuesday night made his third minor league rehabilitation start as he makes his way back from Tommy John surgery on right elbow. Severino went 2 1/3 innings, allowing two runs and two hits while walking one and striking out four.
Severino will continue to build up arm strength. Prior to Tuesday's outing for Double-A Somerset, Severino had been sidelined since June 12 after suffering a strained right groin.
''An encouraging step for Sevy,'' Boone said.
''We don't want to feel like we're rushing him back for a guy that hasn't pitched in the big leagues for close to 20-plus months. You don't want to take him out of his rehab assignment - essentially his spring training - early.''
Orioles: LHP John Means (5-3, 2.84) will be on the mound for Baltimore on Friday against Tampa Bay.
Yankees: LHP Nestor Cortes Jr. (0-0, 1.93) starts for New York on Thursday to open a four-game series against Seattle.
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