The Royals haven't lost no matter who has been on the mound for the last week.Shields eyes his fifth consecutive victory and Kansas City seeks a seventh straight along with a three-game sweep of the Chicago White Sox at U.S. Cellular Field on Sunday.The right-hander had no record and a 7.36 ERA over his previous three starts before beating the New York Yankees last Sunday, giving up an unearned run and striking out eight over six innings of a 2-1 win.Despite the favorable stat line, Shields (7-3, 3.44 ERA) battled through some tough innings -- including a bases-loaded jam in the second -- while allowing six hits and walking two."Shields had to grind it out again and navigate through some choppy waters, but he made huge pitches when he needed to," manager Ned Yost said.The Royals (35-32) haven't lost with Shields on the mound since May 2, and he's 4-0 in seven starts during that span partly because of the Royals' 36 runs of support.The only time Kansas City hasn't scored for him was a 5-1 defeat to Chicago on April 6, when he took the loss despite giving up one run in seven innings. He's 2-2 in his last eight starts against the White Sox despite a 2.03 ERA."Every time he pitches, he puts his heart on the mound and does anything he can to get us a W," third baseman Mike Moustakas said.Moustakas did his part in helping Kansas City set a season high for consecutive wins Saturday, going 3 for 4 with a solo homer and two RBIs in a 9-1 victory. He's hitting .364 with two homers and five RBIs during the Royals' winning streak and has raised his batting average 26 points to .174 since June 1, when he was recalled from the minors.Alcides Escobar is batting .439 during an 11-game hitting streak for the Royals, who have won nine of 10 in Chicago."We've had a couple of big innings the last week or 10 days," Yost said. "Early in the year we get something going we get one or two out of it."While Kansas City is averaging 5.6 runs during its streak, the White Sox (33-36) have been outscored 20-3 during a three-game skid. Their lone run Saturday came on a leadoff homer in the ninth from Paul Konerko, who went 3 for 4."Hopefully it ends (Sunday)," Konerko said. "Good teams and good hitters are going to get their hits. (The Royals) are obviously doing that right now, but we have to try to stop the bleeding."Chicago will look to avoid tying its longest losing streak of the season behind Andre Rienzo, who also hopes to end a personal slump.Rienzo (4-3, 5.25) has lost three straight starts with a 9.00 ERA, and he's failed to get out of the fourth inning in the last two. He gave up seven runs and nine hits in 3 2/3 innings of an 8-4 loss to the Los Angeles Angels on June 6.The right-hander originally was scheduled to start Wednesday against Detroit but was pushed back due to Tuesday's rainout. He's used the layoff to work extensively with pitching coach Don Cooper."I made mistakes the last two games, and I paid for that," Rienzo told the team's official website. "I like the confidence shown in me, and I want to answer that with good games."Rienzo has pitched well against the Royals, going 2-1 with a 3.00 ERA in three starts after giving up two runs in six innings of a 7-6 win May 20.