CLEVELAND (AP) -- Paul Byrd pitched six sharp innings in his first official start of the season and the Cleveland Indians beat the Chicago White Sox 4-0 Saturday. Byrd (1-0) had come within one strike of an abbreviated no-hitter on April 6. That was Cleveland's scheduled home opener -- which was snowed out with two outs in the top of the fifth inning and the Indians leading the Seattle Mariners 4-0. Ironically, Byrd's first pitch against the White Sox was a called strike -- exactly what he needed eight days earlier to make it an official game in a swirling snow at Jacobs Field. Ryan Garko and Josh Barfield connected for their first homers in the second inning off Chicago rookie John Danks (0-2) to put Cleveland ahead 2-0. Garko, who had a career-high four hits in a 6-4 loss to the White Sox on Friday night, led off the inning with a drive into the bleachers in left-center. Two outs later, Barfield hit his first homer in the AL. The second baseman was acquired in a trade from San Diego in November. Byrd allowed five hits, struck out five and issued his only two walks in the fifth. The 36-year-old got two quick outs to get out of that jam, then was at his gritty best in the sixth when the White Sox put runners on second and third with none out but failed to score. Jim Thome got credit for a double when his popup down the left-field line fell safely against the Indians' defense, which was shifted toward right field against the left-handed slugger. Third baseman Andy Marte, playing nearly at the regular shortstop position, overran the popup, then reached back over his shoulder and missed it. Thome went to third on a single up the middle by Paul Konerko. Byrd struck out Jermaine Dye, got Joe Crede to foul out to first and retired A.J. Pierzynski on a popup down the left-field line. Danks allowed seven hits over 5 1-3 innings in his first career road start. The 21-year-old, acquired in a trade from Texas in December, walked one and struck out four. Kelly Shoppach walked and scored on Jason Michaels' two-out triple to center in the seventh. Michaels scored when Travis Hafner reached on an error by second baseman Tadahito Iguchi. Joe Borowski retired Darin Erstad on a foul popup with runners on second and third in the ninth for his fourth save in four chances.