Carter connected for two home runs, Springer set a rookie club record for home runs in a month and the Astros beat the Kansas City Royals 9-3 on Wednesday for their fifth consecutive victory.
The Astros have been waiting for Carter to take off after he hit 29 home runs last year.
"This guy led our offense in home runs and RBIs last year. He had been hot and cold, but we all know when he's hot, he can carry a ballclub because we've seen him do it," Astros manager Bo Porter said.
"We definitely would love to get him going. That would be an added boost to our team," he said.
Carter, who had been benched the previous three games with a .192 batting average, homered to lead off the fifth. He hit a three-run homer in sixth off reliever Louis Coleman for his fourth career multihomer game and his first this season.
"He sat for three days, worked extremely hard in the cage and watched a lot of video," Porter said. "He came in today with a good game plan and understanding the things in which he's worked on the last few days."
"I always say this: It's good from a coaching standpoint you put in effort with a guy and the next time he gets in the lineup you see it pay off. That's good for the player to see the immediate results of the work which he's putting in," he said.
Springer connected off Danny Duffy (2-5) in the first for his ninth home run in May. Glenn Davis held the Astros' rookie record with eight home runs in September 1985. Springer also walked twice and was hit by a pitch.
"Our offense is better," Carter said. "It's been coming around really good. George has six home runs in six games. I'm happy for him. I think we have something going here."
The Astros, with the worst record in the AL, won three times in Kansas City for their first sweep of the season. Houston's winning streak is its longest since a six-game string that ended last June 3.
The Royals have lost four in a row.
"It's just a bad series, unfortunately, it happened at home," Royals designated hitter Billy Butler said. "It's a tough go right now."
Carlos Corporan had three hits with a walk. He drove in a run as the Astros outscored the Royals 21-5 in the series.
Jarred Cosart (4-4) gave up one earned run and four hits in five innings, but was pulled when his pitch count reached 95.
"I chose a good day to go five and the offense scored nine runs," Cosart said. "I didn't have my best stuff. The offense came out scoring early. I felt pretty good out there. I had a couple of innings with high pitch counts. We have a five-game winning streak going. We've got momentum. We're going back home to our own ballpark."
Duffy allowed six runs on seven hits and five walks in four-plus innings. The first four Royals pitchers combined to walk 10, which was a season high.
"He just didn't have anything going for him today," Royals manager Ned Yost said. "His fastball was down to 88-92 (mph) and we kept checking and asking if he was OK. He was fine, but he was going through a little dead arm. He was throwing hard, but it just wasn't coming out. We had to kind of ride it. We didn't have any bullpen help."
Brett Hayes singled in the Kansas City fifth to snap an 0-for-27 skid to begin the season. He homered in the seventh, the Royals' first home run in nine games.
Houston 2B Jose Altuve dropped Eric Hosmer's popup to shallow right in the sixth inning for his first error of the season. That ended an Astros' record of 88 errorless games by a second baseman. Altuve also had a single and tops the majors with 73 hits. ... Butler grounded out four times and is in a 2-for-22 funk, tumbling his average to .235 with one home run. ... Royals LF Alex Gordon batted third for the first time this season and extended his hitting streak to six games with a first-inning single.