It was the first win of the season for the defending NPSL champions in five starts.
The Drillers, coming off a win at Wichita on Friday night, dropped to 3-1.
Edmonton's Alfredo Valente and Milwaukee's Todd Dusosky exchanged goals in the first quarter.
Milwaukee blew the game open in the second quarter on a shootout goal by Steve Morris, two-pointers by Matt Tirschman, Greg Howes, Michael King and Morris, and a three-pointer by Tirschman, giving the Wave a 14-2 lead at the half.
Dusosky added his second two-pointer in the opening minute of the third quarter and Morris made it 16-2 with his third goal, at 5:28.
Martin Dugas ended the string of Milwaukee goals off a pass from Sipho Sibiya with just over a minute remaining in the third, but Tirschman capped the scoring at 11:09 of the fourth with his third goal.
The Drillers, who play at Wichita again on Monday morning, now are 0-8 in Milwaukee.