This is what catharsis looks like.

It is a mighty swing at an 83-mph slider from an old rival on a new team. It is a baseball following the arc of a rainbow before touching down in the right field bleachers. And it is David Ortiz making the slow trot around the bases in the ninth inning, then returning to a Red Sox dugout filled with teammates who were equal parts ecstatic and relieved.

One week after their last victory, two outs from dropping their sixth consecutive game, the Red Sox rode a three-run homer from Ortiz against Detroit Tigers reliever Joba Chamberlain, late of the New York Yankees, to a 5-3 victory here in the finale of a three-game series.

And if it’s premature to call Game No. 60 a must-win, it was darn close.

Consider all that had gone wrong — in this one game — before Ortiz’ blast:

•   The Red Sox were 1-for-11 with runners in scoring position, leaving two men on base in the third inning, two more in the fourth, two in the seventh and two in the eighth.

•   In the sixth inning, catcher A.J. Pierzynski overran second base and was doubled off, ending another potential rally.