The victory moves Kitchener one point behind Owen Sound for third place in the Western Conference standings.
Jared Gilbert scored his first-career OHL goal at 4:38 of the second period for the Rangers (36-17-8), who have won three games in a row, while Joel Vienneau stopped 37 shots for the victory.
Cameron Brace responded for the Attack (38-18-5) with a power-play goal at 14:57 of the third period to force extra time.
Jordan Binnington earned the game's first star after turning away 40-of-41 shots in defeat.
Kitchener went 0 for 3 on the power play while Owen Sound scored once on four chances with the man advantage.