Jones (3-0) came in with two outs in the fourth inning following the ejection of Chisox starter Jose Quintana and held the Rays to two runs over two innings.
Matt Thornton and Jesse Crain combined for 2 1/3 frames of scoreless ball and Addison Reed picked up his sixth save as American League Central-leading Chicago won its eighth straight and swept the Rays at Tropicana Field for the first time since 2007.
Home plate umpire Mark Wegner tossed Quintana after the rookie left-hander, while making only his second career start, threw a pitch behind batter Ben Zobrist.
White Sox Manager Robin Ventura was also ejected for arguing the call.
Dayan Viciedo went 3-for-4 with an RBI while Alex Rios added two hits, including a first-inning RBI single, in the victory.
Rays starter Alex Cobb (2-1) was touched for four runs on nine hits over five innings.
Notable deaths of 2014 [PHOTOS]