Steven Gerrard arguably earned his best result in six matches as manager of the Scottish giants as goals from Alfredo Morelos, James Tavernier and Lassana Coulibaly gave Rangers an excellent chance of progressing.
Almost a sell-out, 48,001 fans crammed into the 50,000-capacity Ibrox to watch on as Rangers dominated from start to finish and arguably should have scored more - Morelos straying offside in what should have been an easy goal.
Beale, who joined the club after working with Gerrard at Liverpool following a short stint in Brazil with Sao Paulo, was full of praise for the Rangers fans as he reacted on Twitter to the win.
Outstanding support from the fans tonight at Ibrox. You pushed the team forward for the full 90+ minutes ⚪️ nothing is won yet. Still a lot to play for next week.— Michael Beale (@MichaelBeale) August 9, 2018
Rangers now face newly-promoted St. Mirren who are managed by former Celtic defender Alan Stubbs, and will also have a rivalry with the likes of Beale and Gerrard due to his two spells at Everton as a player.
The Gers then travel to Slovenia next week in a bid to see out the tie against Maribor, with the prize being a place in the Europa League qualifying play-offs.
Gerrard's side will face Russian outfit UFA or face another test against Progres Niederkorn - the side that embarrassingly knocked Rangers out at the first qualifying stage last term. UFA won 2-1 in Russia on Thursday.