Alberto Callaspo laced a double off Matt Thornton (3-7) with two outs in the 10th inning and came in to score the deciding run on Kendrick's single to shallow right field.
Ernesto Frieri protected the lead with 1-2-3 bottom of the 10th for his 13th save as the Angels evened their three-game series with the American League Central-leading White Sox.
Kevin Jepsen (2-1) was credited with the victory with a scoreless ninth.
Kendrick finished with two RBI and Albert Pujols also drove in a pair, including a solo homer, enabling Los Angeles to tie Oakland for the AL wild card lead.
Coupled with Detroit's win Saturday, the Chisox saw their AL Central lead over the Tigers shrink to 1 1/2 games with the setback.
Celebrity Families of 2014 [PHOTOS]