The Generals (8-4, 6-0 ODAC) scored their first goal 85 seconds in, led 3-0 by the 11:51 mark and scored one more time before SU (8-6, 3-4) got on the board.
W&L, on the strength of two goals in the final 72 seconds of the opening stanza, took a 7-3 lead into the second.
LaTona and Connor Bishop had the hosts goals in a closing flurry that featured five goals in the final 2:30 of the period. LaTona's tally, with 21 seconds to go and off of a Schott assist, was his program record-breaking 47th of the season. The senior broke the mark he co-held with Justin Ratcliff '07.
The Generals took a 13-5 lead into the half and erased any thoughts of an SU comeback by scoring the initial seven goals of the third period.
Schott, with an unassisted goal at 22 seconds, had the only goal of the quarter for Shenandoah.
Washington and Lee outscored the Hornets 5-3 in the final 15 minutes.
The Generals outshot SU 62-29, won 30-of-38 faceoffs and had a 44-16 advantage in groundballs.
Ben Judy had 13 saves in just more than 35 minutes of action. The Shenandoah goalies combined for 20 saves.
Schott led the offense with three goals and one assist.