White Sox rookie Dylan Covey (0-5) walked the bases loaded before the Moss grand slam in the first inning.
Gaviglio is making his second start since joining the Royals and settled for a no-decision in the first after allowing one run and four hits over five innings against Minnesota.
It might make sense for general manager Rick Hahn to entertain offers this offseason not only for Abreu but right fielder Avisail Garcia, who is enjoying his best season but is also under club control through 2019.
Jose Abreu is in the midst of a tear and looks to record his fourth consecutive stellar performance when the ChicagoWhite Sox visit the Kansas City Royals on Tuesday for the middle contest of their three-game set. And Abreu will be 33 when he signs his next big contract, which could be an expensive deal should he continue at the steady, productive pace he's on now.
The ChicagoWhite Sox have enjoyed a little surge where both the arms and bats have been productive. He saw action in 22 games with Salt Lake, the Angels' Triple-A affiliate, going 0-1 with a 3.20 ERA.
In conjunction with Major League Baseball, the Kansas City Royals today announced their 2018 regular season schedule.
Moss finished with two hits and over the last three games and is 6 for 9 with three homers, a double and nine RBIs.
Giants: RHP Chris Stratton (2-3, 4.10 ERA) will oppose Dodgers RHP Kenta Maeda (12-6, 4.02 ERA) in the opener of a three-game series in San Francisco. Hammel lasted just three and a third innings, coughing up five runs, walking two and striking out seven.