CHICAGO -- As soon as he stepped on the mound, Jake Odorizzi went on the attack. Jason McCourty Jersey . And nobody could stop him. Odorizzi struck out nine in six scoreless innings and combined with two relievers on a five-hitter to lead the Tampa Bay Rays to a 4-0 victory over the Chicago Cubs on Saturday. "The first at-bat itself I felt like I was throwing it where I wanted to, and once it carries over to the next batter you kind of know you have that going today," he said. Evan Longoria drove in a run and scored two. Yunel Escobar added two hits and three RBIs. Ben Zobrist had two hits and scored twice for the Rays, who improved to a major league-best 15-6 since July 12. They will try to complete the three-game sweep on Sunday. "If we keep the nose down and keep playing well, youre going to look up at some point and all of a sudden people are going to say, Hey, youre getting pretty close," manager Joe Maddon said. Odorizzi (8-9) gave up three hits and didnt walk anyone. The right-hander came within two strikeouts of his career high after getting hit hard in a loss to the Los Angeles Angels on Sunday. Chicago starter Edwin Jackson (6-12) allowed four runs -- three earned -- and five hits in six innings. He is 1-5 in his past nine starts. Cubs prized prospect Javier Baez doubled but had a tough day overall, going 1 for 4 and committing his first error. He had three strikeouts after whiffing four times Friday in his Wrigley Field debut. The second basemans error came when he dropped a throw from Luis Valbuena after the third baseman made a diving stop on a ball hit by Longoria with a runner on first in the sixth inning. Jackson then walked Matt Joyce to load the bases, and Escobar made it 4-0 with a two-run single. The Rays also scored two in the fourth when Longoria doubled in a run and came around on Escobars base hit. Kirby Yates pitched two perfect innings, striking out three. Jake McGee then gave up two hits but struck out three in a scoreless ninth. The Rays took a 2-0 lead in a fourth inning that featured some unusual plays. Zobrist led off with a ground-rule double to the right-field corner off Justin Ruggianos glove that stuck in the ivy. He moved up when centre fielder Arismendy Alcantara dove to his left to snag James Loneys liner and came around on Longorias double. Escobar added a two-out RBI single that Ruggiano pulled up on before making a flat-footed throw to the infield with the runner headed home. "It was just a mental mistake by me," he said. TRAINERS ROOM Rays: Outfielder Wil Myers (broken right wrist) was scheduled to start a rehab assignment Saturday with Triple-A Durham and serve as the designated hitter. Cubs: Manager Rick Renteria said newcomer Felix Doubront (strained left calf) "looked good" during a bullpen session but had no word on a possible rehab assignment. The left-hander was acquired from Boston on July 30. ON DECK Rays: Right-hander Alex Cobb (7-6, 3.52 ERA) looks to continue his strong stretch as the Rays wrap up their three-game series against the Cubs. He has allowed two runs or fewer in five straight starts. Cubs: Left-hander Travis Wood (7-9, 5.08) looks for his first victory in nearly two months. An All-Star last season, Wood is 0-4 with a 6.10 ERA in nine starts since a win at Philadelphia on June 15. A LITTLE EARLY MLB Advanced Media, using the Cubs Twitter account, jumped the gun a little bit when it posted the Rays beat Chicago 4-0. That turned out to be accurate, but the problem was the game was still in the ninth inning. They later Tweeted an apology. DESIGNS ON SUCCESS With the Cubs wearing throwback uniforms from 1988 on Sunday, the Rays will also go retro -- sort of. Tampa Bay will wear uniforms with light blue shirts and pants, yellow sleeves and dark blue accents suggesting what the team would have worn had it existed in the 1980s. The designer? Owner Stuart Sternberg. 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