Josh Anderson opened the scoring for London short-handed at 14:03 of the first, but Owen Sound's Daniel Milne tied it before the end of period with an even-strength goal.
Zach Nastasiuk put the Attack ahead a minute into the second with a power-play goal, his 17th of the season.
However, London once again tied the game when winger Bo Horvat scored his 30th of the season at 17:27.
Tied 2-2 in the third, Brayden Rose netted his first of the season to put Owen Sound in position to win, but Remi Elie forced overtime when he scored for the Knights at 15:10.
London improved to 47-12-4 and leads the Western Division with 98 points.
Jordan Binnington made 30 saves for the Attack (39-18-6), who are third in the West.