Fielder ended 4-for-5 with a solo homer, while Avila was 4-for-4 with two runs scored for the Tigers, who put the brakes on a three-game skid and rebounded from a loss in Monday's opener.
Rick Porcello (12-8) went the distance for the first time in his career, giving up one run on seven hits with five strikeouts.
Conor Gillaspie totaled two hits and drove in the lone run for the White Sox, who had won two in a row.
Erik Johnson (0-2) was pulled after 3 2/3 frames, having allowed seven hits and six runs, though only two were earned -- with four strikeouts and three walks.
Detroit picked up two runs in the first. Andy Dirks singled with one out then advanced on a passed ball before scoring on a Gillaspie throwing error on a Miguel Cabrera grounder. Fielder singled to put runners on the corners and a Martinez fly to left made it 2-0.
Jackson doubled to start the fourth and scored on a two-out hit from Fielder, then after a wild pitch and walk to Martinez, Johnson was finally lifted from the contest down 6-0.
Chicago answered in the home fourth, as three straight singles, the last from Gillaspie, plated Konerko, whose one-out hit started the sequence.
The Tigers roared back in the fifth, when Avila doubled, moved to third on a Jose Iglesias grounder and scored on a Gillaspie error.
It was 9-1 in the ninth as an Iglesias base hit with runners on first and second sent one run home and Jackson followed with a base hit to score Avila.
Detroit has won nine of 15 from Chicago this season, and five of nine on the south side of America's third-largest city ... Porcello's longest previous outing this season was an eight-inning scoreless foray in a 1-0 loss to Pittsburgh on May 28, during which he fanned a season-high 11 batters ...Detroit announced on Tuesday that shortstop Jhonny Peralta, currently serving the latter portion of his 50-game suspension for a violation of MLB's drug policy, will join the club on Wednesday ... Prior to the game, the Tigers recalled pitcher Darin Downs from Triple-A Toledo.