The Indians batted around in a five-run first against Kyle Davies before Sizemore led off the second with his 22nd home run. Martinez homered with two outs to make it 7-0.
"It was great to have that cushion going out there in the first inning," Laffey said. "It was definitely a plus. I kept getting up to give guys high fives coming in the dugout. It makes you a little more comfortable every time a run scores."
The night before, the Indians mustered only one run for ace C.C. Sabathia, who allowed only two runs in eight innings.
On Saturday night, the Indians turned three double plays behind Laffey, while the outfield made just one putout -- Ross Gload flied out to Sizemore with two outs in the eighth -- the entire game.
"It's just a combination of throwing the sinker and being able to throw the changeup behind the sinker, two different speeds and both have late down action on them," Laffey said. "That really helps to bust guys in and then go away and get them to pound it into the ground. I was really able to throw my changeup for strikes in all counts, that really helped me today. I didn't have great fastball command."
The Indians, who lead the Detroit Tigers by 2 ½ games in the AL Central, scored three runs or less in 18 of their previous 29 games while hitting just .238.
"It was good the way we came out and to see us put up the type of ABs and hit the ball the way they did," Indians manager Eric Wedge said. "Now we've got to start putting days together. Our guys up top led us and Kenny (Lofton) did a great job at the bottom of the order, as well as Franklin Gutierrez."
Laffey (2-1) held the Royals to two runs and eight hits -- all singles -- to win his second straight start.
"We can't seem to get one in the gap or over the fence," Royals manager Buddy Bell said.
Davies (1-2) got roughed up again in his fifth start since the Royals acquired him in a July 31 trade with Atlanta, lasting just two innings and throwing 44 pitches in the first. Davies gave up seven runs and eight hits with a walk. He has a 7.48 ERA since joining the Royals.
"That's the first time I've ever went through that many pitches in the first inning," Davies said. "I couldn't throw my curveball over and couldn't establish the slider or the changeup. Big league hitters sit on fastballs. They can hit them. You have to pitch ahead, and you have to establish the fastball early."
Sizemore led off the game with a double and scored on Asdrubal Caberera's single. Martinez doubled home Travis Hafner, who had walked, and Jhonny Peralta's single scored Martinez. After Kenny Lofton singled for his 2,400th career hit, Gutierrez had a two-run double.
"It's another ball for the mantel," Lofton said.
Lofton doubled in the fifth and scored on Casey Blake's single. It was Lofton's sixth multihit game in 24 games since being traded on July 27 to the Indians.
Emil Brown went 4-for-4, his second career four-hit game.
Right-hander Billy Buckner, who replaced Davies, made his major league debut and held the Indians to one run and seven hits over five innings, while walking one and striking out one.
David DeJesus added a two-run double in the ninth.
- DeJesus was hit by a pitch from Laffey in the third inning, tying him for the league lead with 16. The Royals record for a season is 18.
- Royals DH Mike Sweeney, who had knee surgery last month, went 1-for-3 on Saturday in his second minor league rehab game with Triple-A Omaha.
- Indians starting pitchers have gone at least five innings in 113 of 128 games. Cleveland starters lead the league with 805 innings.
- Brown's other four-hit game was July 11, 2005, at Arizona.