Maybe the Royals were just waiting for Independence Day to generate some offensive fireworks. Or perhaps they were simply overdue.</p><p>Either way, they marked the holiday Saturday afternoon by overcoming a three-run deficit in a 6-4 victory over the Chicago White Sox at Kauffman Stadium.</p><p>Alberto Callaspo led the comeback with an RBI triple in the fifth inning that provided the Royals with their first run in 14 innings. He then blooped a two-run single that capped a decisive three-run sixth.</p><p>There was more: An eighth-inning homer from Brayan Pe&ntilde;a, a Cuban native celebrating his first Fourth of July as an American citizen, and air-tight relief from a three-man bullpen relay.</p><p>It all enabled the Royals &mdash; for one day anyway &mdash; to shed some frustration.</p><p>&ldquo;Once we got things going &hellip;,&rdquo; center fielder Mitch Maier said. &ldquo;That&rsquo;s something we haven&rsquo;t been able to do the last few days. The way all of our pitchers have pitched, they&rsquo;ve kept us in every game. We just haven&rsquo;t been able to produce offensively.&rdquo;</p><p> The six runs marked the Royals&rsquo; biggest output in 20 days &mdash; since a 7-1 victory over Cincinnati on June 14. It also snapped a four-game skid in which they scored just three runs.</p><p> &ldquo;Guys just kept grinding,&rdquo; manager Trey Hillman said, &ldquo;and gave good plate appearances.&rdquo;</p><p> The Royals, 34-46, managed just seven hits but still overcame a three-run deficit for the first time since May 19, when a four-run rally in the ninth inning produced a 6-5 victory over Cleveland.</p><p> &ldquo;They put a couple of good innings together,&rdquo; Chicago manager Ozzie Guillen said. &ldquo;They got big hits. They got clutch hitting. Callaspo&rsquo;s hit, that was big.&rdquo;</p><p> The Royals&rsquo; Luke Hochevar allowed four runs and nine hits in six innings, the 11th time in 12 games a starter worked at least six innings.</p><p> &ldquo;We swung the bats well,&rdquo; Hochevar said. &ldquo;We played great defense, and the bullpen did an outstanding job. We&rsquo;ve been playing hard. It hasn&rsquo;t been a matter of that. We just finally got some hits to fall at the right times.&rdquo;</p><p> Hochevar, 4-3, got the victory when Juan Cruz, John Bale and Joakim Soria retired all nine hitters over the final three innings. Soria got his 11th save in 13 opportunities &mdash; and his third successive one-two-three save.</p><p> &ldquo;Everyone looked good today,&rdquo; Soria said. &ldquo;That&rsquo;s important to us. When we start feeling like that, we&rsquo;ll start winning some games.&rdquo;</p><p> The White Sox, in search of an eighth straight victory, opened the scoring on DeWayne Wise&rsquo;s two-out RBI single in the second inning. Jermaine Dye made it 3-0 with a two-run homer in the third.</p><p> Chicago starter Gavin Floyd, 6-6, didn&rsquo;t yield a hit until Mike Jacobs opened the fifth inning with a clean single to right field. Callaspo followed with an RBI triple, and Maier&rsquo;s one-out sacrifice fly made it 3-2.</p><p> Hochevar surrendered a one-out homer to rookie Gordon Beckham in the sixth, but Floyd failed to survive the Royals&rsquo; half of the inning.</p><p> Willie Bloomquist led off with a single, and Billy Butler walked. Jos&eacute; Guillen&rsquo;s grounder to second resulted in a force at second base &mdash; but no double play thanks, in part, to Butler&rsquo;s nice takeout slide &mdash; and Mark Teahen delivered an RBI single up the middle.</p><p> That finished Floyd,</p><p> Pe&ntilde;a batted for Jacobs and moved the runners to second and third on a weak grounder to third against reliever Matt Thornton. Callaspo then served a soft two-run single into right for a 5-4 lead.