Carpenter tops the National League with 32 home runs, a .600 slugging percentage and 65 extra-base hits. He has reached base in a career-high 28 straight games with 16 homers and 27 RBI in that span.
"It's fun to watch, that's for sure," Cardinals interim manager Mike Shildt said. "Clearly, he's a special player, a special guy. I'm just happy for him. He's always looking to grow from the previous version of Matt Carpenter."
Carpenter sent a fastball from Burch Smith into the right-field fountains for a two-out drive with Harrison Bader aboard. He extended his career high for homers as the Cardinals scored five times in the second.
"Just having Harrison on base in front of me, just his speed alone you've got to figure bought me maybe an extra fastball or so," Carpenter said. "It's a big part of it."
Bader homered in the sixth and Martinez had an RBI double in the seventh.
Gomber (2-0) allowed four hits, walked one, hit a batter and struck out three in his third major league start.
"It makes my job a lot easier, especially when my game plan is attack and throw strikes," Gomber said of the big lead.
Daniel Poncedeleon allowed two hits over three innings to notch his first big league save.
Gomber worked out of a bases-loaded jam in third, which Adalberto Mondesi led off with a triple. After retiring the next two batters, Gomber walked Rosell Herrera and hit Salvador Perez with a pitch. Hunter Dozier flied out to end the inning.
"We couldn't capitalize on it," Royals manager Ned Yost said.
Smith (1-4) gave up five runs on six hits, a walk and a hit batter in 1 2/3 innings. In six starts, Smith has a 9.67 ERA, allowing 24 earned runs in 22 1/3 innings.
"I wasn't commanding any pitches," Smith said. "I just didn't have anything working and they were capitalizing on mistakes. They're good hitters. I just didn't have it."
The Royals stranded 11 runners and went 0 for 8 with runners in scoring position. Kansas City has lost seven of eight.
Royals LF Alex Gordon, who hit .366 with six multihit games in the past 11 games he had started, was not in the lineup. Yost said he wanted to give Gordon two straight days off with the club idle Thursday.
Cardinals: RF Yairo Munoz left in the sixth inning with a sprained right wrist after swinging at a pitch. Adolis Garcia replaced Munoz and singled in the eighth for his first big league hit. ... OF Tyler O'Neill (right groin inflammation) began a rehab assignment with Triple-A Memphis. He went 2-for-4 with a two-run double and struck out twice at Oklahoma City. ... RHP John Brebbia (right forearm tightness) was placed on the disabled list retroactive to Monday. ... RHP Adam Wainwright (right elbow inflammation) threw batting practice at the club's complex in Jupiter, Florida. "All reports of that were favorable," Shildt said. "We'll see how he recovers." He said the team is evaluating whether Wainwright throws another batting practice or begins a minor league rehab assignment.
Royals: OF Brian Gordon (left groin strain) ran the bases as his final hurdle before coming off the disabled list. He said he is at about 80 percent.
Cardinals: Rookie RHP Jack Flaherty is 5-6 with a 3.27 ERA in 18 starts.
Royals: LHP Danny Duffy will be facing the Cardinals for the first time since June 27, 2016.
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