Following Rangers' lackluster performance against Montenegrin club FK Zeta in Champions League qualifying on Wednesday -- a 2-0 win at Ibrox -- Charlie Adam was dropped, and Beasley replaced him on the left wing.
Beasley had a chance to put Rangers ahead early in the game when he broke free of the Inverness defense, but he couldn't beat goalie Michael Fraser from a tight angle.
Barry Ferguson put Rangers ahead minutes later, and substitute Nacho Novo and Ferguson scored to seal the victory.
Rangers got more good news on Sunday: defending champion Celtic could only tie Kilmarnock, 0-0, at home.
Aug. 4 in Inverness
Inverness 0 Rangers 3. Goals: Ferguson 16, 90, Novo 64.
Inverness -- Fraser, Tokely, McCaffrey, Munro, Hastings, McBain (Hart 70), Wilson, Black, McAllister (Cowie, 62), Wyness, Rankin (McDonald, 77).
Rangers -- McGregor, Hutton, Cuellar, Weir, Papac, Thomson, Ferguson, Hemdani, McCulloch, Boyd (Novo 49), Beasley.
Referee: Kenny Clarke.