Engel assisted both goals for Loyola (5-6-2, 2-3-0 Patriot League), while senior Connor Thompson was responsible for the Greyhounds' first goal.
In the 24th minute, Engel intercepted a pass on the left wing and he played it between defenders to Thompson just inside the top-right side of the box. Thompson one-touched the ball and fired a 16-yard shot into the left side of the net for the game's first goal.
Lehigh (6-7-0, 2-3-0) tied it up in the 53rd minute though, when a ball bounced to Ali Famili after a scramble inside the small box. Doyle Tuvesson had his initial shot blocked, but he was able to recover the rebound just off the left post and get it to Famili at the top of the box for the equalizer.
The Greyhounds had a pair of scoring chances throughout the remainder of regulation, but were unable to capitalize on the opportunities. In the 60th minute, Thompson played a free kick from the right side to junior Antony Sare inside the small box. Sare was unable to turn the pass though, with his shot missing the near post.
Sophomore Laurin Vogel then had a shot from the left side roll into the arms of Ciaran Nugent, Lehigh's goalkeeper, in the 87th minute.
As time expired in the first overtime period, the Mountain Hawks looked to have secured the victory, as Brian Vail put away a free kick from Jamie Luchini, but Vail was flagged offsides, negating the goal.
Cahalan then headed in the game-winning goal, his second of the season, in the 107th minute to improve Loyola's record to 4-1-0 at home this season. Engel had dribbled down the right sideline before shaking off a defender and sending a left-footed cross into the box, which Cahalan was able to beat his defender to.
The Mountain Hawks held a 14-9 advantage in shots and a 7-2 lead in corner kicks thoughout the game, but sophomore Matt Sanchez came up with five saves in goal for Loyola. Nugent finished with three saves for Lehigh.
The Greyhounds will remain home for a second-straight contest as they host Boston University next Saturday at 7 p.m.