If their season-long pattern holds true, the Chicago Cubs will now go out and win 10 of their next 12 games.
"It's been really streaky the first half," said manager Jim Riggelman. "That's not going to get it done."
After winning 10 in a row May 29-June 8, the Cubs had lost 13 of 17 before Sunday's victory. They began the season 8-2, then went 5-11, then won 14 of 19, then lost six of seven.
"We've got to find a way to be more consistent. This ballclub and this organization have been so mediocre for so long," Riggelman said.
"We won 10 in a row. We had people setting records, then all of a sudden we're reading in the paper how great we are. Then we look up two weeks later and you wonder how you ever won a ballgame. This has been a terrible streak.'
Sammy Sosa had two singles and an RBI for the Cubs, but he failed to homer for a third straight game.
Sosa, whose 19 homers in June are a major league record for homers in any month, increased his RBI total to 78 with a single in the fifth off Pat Rapp (7-7). But the Cubs outfielder, whose 32 home runs are second in the majors to Mark McGwire's 36, has now gone three games without a homer for the first time in two weeks.
The Royals, who took two out of three from the Cubs, had their first winning homestand of the season and drew more than 20,000 per game over their average this season. The 112,590 attendance for the series was the largest for a three-game set in Kansas City since 1989.
"It makes difference," said first baseman Jeff King. "The atmosphere is more exciting. The games seem like they mean a little more when you've got a packed house."
Jeremi Gonzalez (7-5) gave up eight hits and three runs in 5 1-3 innings, and Terry Mulholland pitched three scoreless innings for the Cubs. Rod Beck got Dean Palmer to ground into a game-ending forceout with runners at the corners to pick up his 18th save.
"We had no choice today, We had to win," Beck said. "We're so tired of losing and we've got a day off tomorrow and everybody wants to have a nice day off."
Rapp lasted 4 2-3 innings, giving up five runs and five walks.
Mark Grace, who turned 34 Sunday, walked leading off the second and eventually scored on Kevin Orie's fielder's choice grounder. Second baseman Jose Offerman's throwing error on the play also allowed Tyler Houston to score.
After Sosa's RBI single put the Cubs on top 3-0 in the third, Manny Alexander made it 4-0 in the fifth with a leadoff homer.
The Royals got all their runs on solo home runs, by Jeff Conine in the fifth, and Dean Palmer and Shane Mack in the sixth.
Orie's RBI double in the sixth put the Cubs ahead 5-1. In the eighth, Henry Rodriguez singled, went to second on a wild pitch, took third on Mike Sweeney's throwing error and scored on Matt Whisenant's second wild pitch.
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