Moreland hit two home runs in a second straight game, and Texas celebrated the return of Josh Hamilton with an 8-6 victory Tuesday night.
Shin-Soo Choo and Robinson Chirinos also went deep for the Rangers, who have hit eight home runs over the past two nights.
"There is no defense for a home run," Texas manager Jeff Banister said. "I like to see it. They're quick runs. When they come, we'll take them."
Moreland homered with a man on in the second and eighth innings. It's the eighth time in club history that a player has hit multiple home runs in consecutive games.
"I'm trying to go up there and see it well, get ready to hit," Moreland said. "Couple of them have been maybe a little helped by the ballpark. It's a great hitters' park."
Hamilton hit two singles and made a nice running catch of a sinking liner to left field in his eighth game of the season. The free-swinging slugger was sidelined since May 31 with a strained left hamstring.
"I am trying to barrel on the ball. You start from there," Hamilton said. "Once you start from there, you try to put a little extra into it if you need to. Overall, I felt good with my at-bats. It was a good night overall."
Over their first 76 games, the Rangers had one game with four home runs. Now they have three.
"We're starting to get some guys back in the lineup," Banister said. "We got Hamilton back in there and (he'll) be able to provide that offense for us and stretch that lineup out. This is an offense that can be dangerous and powerful at times."
Chris Davis hit two home runs for Baltimore and Manny Machado added a solo shot. The Orioles have lost two straight following a four-game winning streak.
"We scored, what, six runs? There was enough to win a baseball game," manager Buck Showalter said. "They just did a better job, pitched a little better."
Colby Lewis (8-3) allowed five runs, three earned, and six hits over six innings to improve to 4-0 in six starts since May 27. He was tagged for three homers but survived the onslaught.
Shawn Tolleson gave up a run in the ninth but picked up his 11th save.
Miguel Gonzalez (6-5) surrendered six runs and eight hits in 4 1/3 innings, including a career-high tying three homers. The six runs were the most he allowed since April 4, 2014, when he gave up seven to Detroit.
The Orioles jumped in front in the first inning when Texas second baseman Rougned Odor fumbled a two-out grounder and Davis homered to extend his hitting streak to 10 games.
Moreland tied it in the second after a welcome-back single by Hamilton.
Texas went up 4-2 in the third when Prince Fielder singled in a run and Odor scored on a double-play grounder. Davis made it 4-4 in the bottom half with another drive to center following a two-out single by Adam Jones.
The long-ball barrage resumed in the fifth, when Chirinos led off with a homer and Choo connected on an 0-2 pitch.
Machado homered in the bottom half to get Baltimore to 6-5. Moreland's drive off Chaz Roe in the eighth gave him his seventh career multihomer game.
He leads Texas with 14 home runs and ranks second with 43 RBIs.
Rangers: Texas has hit four home runs in consecutive games for first time since Sept. 2-3, 2012.
Orioles: Davis has nine career multihomer games, two this season (May 27 against Houston).
Rangers: LHP Derek Holland, who injured his left shoulder in the opener and has not pitched since, is expected to undergo another MRI this week. If there are no problems, he can begin throwing off the mound.
Orioles: 2B Jonathan Schoop (knee) is ready to return from the DL but will finish up his rehab stint with Class A Frederick before the Orioles make a move at the end of the week.
Rangers: RHP Nick Martinez (5-4, 3.39 ERA) pitches in the third game of the series Wednesday night. He gave up a career-high nine runs in his last start vs. Toronto.
Orioles: Wei-Yin Chen (3-4, 2.90) starts for Baltimore, looking to improve his 4-0 lifetime record against Texas.