Scott Lord, Karl Zaengle and Day each scored inside the first 10 minutes en route to a 3-0 lead for Greene at halftime.
Conner Moriarity and Marcus Lindstrom made one save apiece in the combined shutout for the Trojans, who had advantages of 24-9 in shots and 12-1 in corner kicks.
Matt Olin had 11 saves and Kyle Hinman contributed three for the Crimson Knights (1-5-1, 1-5-1), who host Unatego on Saturday.
Walton 3, UV 0
Jared Beach and Chad Swartwout each had a goal and an assist to lead host Walton to its third straight victory in the MAC.
Swartwout scored unassisted on a 25-yard shot nine minutes into the game. He then set up Beach for a goal to the far post from inside the box with 5:21 left before halftime.
Beach assisted Nate Pieper a little more than two minutes later for a goal that gave Walton a 3-0 cushion at the break.
Dylan Walley (seven saves) and Dan Cucciarre (one save) combined on the shutout for the Warriors (8-2, 6-2), who host Sidney on Monday.