Brindza connected on kicks of 26, 25 and 49 yards after the Fighting Irish (9-4) had begun the second half locked in a 13-13 tie.
Tommy Rees completed 27-of-47 passes for 319 yards with no interceptions and Tarean Folston scored on a 3-yard touchdown run in the fourth quarter as Notre Dame improved to 17-6-3 all-time in Yankee Stadium.
Linebacker Dan Fox sealed the victory with an interception of Chas Dodd with 3:28 remaining -- one of three pick-offs for the Irish.
Notre Dame won without running back George Atkinson III and reserve cornerback Jalen Brown, who were suspended prior to the game. Coach Brian Kelly did not disclose a reason.
Dodd completed 10-of-28 attempts for 156 yards with a TD for Rutgers (6-7), which committed four turnovers in all.