Kershaw made quick work of the first batter he faced, striking out Adam Eaton on three straight pitches to end the two-on, two-out threat. But the tide turned in the subsequent frame when the 31-year-old left-hander coughed up back-to-back home runs to Anthony Rendon and Juan Soto.
After facing three batters and only retiring one, righty Kenta Maeda relieved Kershaw in the eighth inning with the score deadlocked at 3-3.
Buehler had thrown 117 pitches when Dave Roberts exited the dugout to summon Kershaw, allowing one run on four hits with three walks while punching out seven over 6 2/3 frames.
Kershaw last appeared in Game 2 of the series on Friday, taking the loss while allowing three runs on six hits with one walk over six innings.
For his career, Kershaw owned a 4.33 ERA over 158 postseason innings entering Wednesday's must-win tilt.