Purcell scored a pair of goals and added an assist for the Monarchs, while Parse recorded a goal and two helpers.
The Monarchs netted two markers in the first period, three in the second, and two more in the final stanza to post their highest goal total of the campaign.
Manchester went 2-for-3 on the power play, and goaltender Jonathan Quick made 29 saves in the winning effort.
The Monarchs go for a perfect road trip when their five-game voyage concludes on Wednesday in Grand Rapids.
Chicago’s three-game home winning streak came to an end.
HAMILTON 5, SAN ANTONIO 3
Rookie Max Pacioretty broke a 3-3 tie with 7:34 left in regulation, and Hamilton went on to a 5-3 road win over struggling San Antonio at the AT&T Center.
Ryan White tallied two of the Bulldogs’ three first-period goals and added an assist for a three-point night.
Bulldogs goaltender Marc Denis turned aside 34 shots to pick up the win, which was Hamilton’s third in a row, all on the road.