In the top of the 13th, Brock Holt worked a leadoff walk for the Red Sox and stole second base. He scored on Scott Alexander's error. Eduardo Nunez hit a grounder on the infield, Alexander scooped and threw to first, but his throw sailed over Enrique Hernandez at the bag, allowing Holt to score from second to give Boston a 2-1 lead.
Here's the Alexander error that gave the Red Sox the lead in the top of the 13th:
Ouch, that hurts. First baseman Max Muncy came in to get the ball and that left it up to Hernandez, the second baseman, to hustle over to first base. Alexander should've just held on to the ball rather than force the throw. It would've given the Red Sox runners on the corners with no outs, but that's better than a runner on first with no outs and a run in.
Not to be outdone, Ian Kinsler gifted the Dodgers the game-tying run in the bottom of the 13th with an error. Muncy worked a leadoff walk and took second base when Nunez caught a pop-up in foul territory and tumbled into the stands. Nunez made the catch on the field and his momentum took him into the stands, and that gave Muncy enough time to tag up.
With two outs and the tying run on second, the Red Sox opted to pitch to Yasiel Puig rather than intentionally walk him to face the light-hitting Austin Barnes. A questionable decision for sure. Puig hit a ground ball to second, Kinsler reeled it in, and rushed the throw to first base. It went wide and Muncy was able to score from second.
Here is Kinsler's error that allowed the Dodgers to tie the game 2-2 in the bottom of the 13th:
Sure looks like the typically sure-handed Kinsler had more time than he seemed to realize. He might've even been able to set his feet. At the very least, he could've taken another step or two to get better better footing. Bad throw by Alexander, bad throw by Kinsler. The Red Sox and Dodgers helped each other survive that 13th inning and live to play another inning.