Steven Smith claimed only his second ever career goal - the other also coming against the Pars in 2006 - before the youngster came off the bench to seal the points with a last-minute strike.
The majority of fans inside Ibrox also used this match to show their support for reinvestment by former director Dave King, via a card display, after blue cards were distributed beforehand by The Union Of Fans.
The South Africa-based businessman - who lost £20million when Rangers went into liquidation in 2012 - found himself on a collision course with the current board recently when he voiced concerns over the club's finances.
As the off-field drama continued to rumble on in the background, the Light Blues were keen to maintain the feel-good factor on the pitch with another win after wrapping up the title against Airdrie in midweek.
Skipper Lee McCulloch started up front, with attackers David Templeton and Andy Little both sidelined after picking up injuries against the Diamonds.
And, with Monday's clash with Albion Rovers in mind, Jon Daly and Lee Wallace dropped to the bench, while Nicky Law was absent from the squad.
Pars players formed a guard of honour ahead of kick-off to acknowledge their hosts' title success - before immediately finding themselves under pressure once the game was under way.
Ian Black whipped a dangerous cross from the right into the box where Nicky Clark connected with the header but he was unable to keep the effort down and on target.
The visitors then suffered a setback when goalkeeper Ryan Scully was injured while defending another attack, and he was forced out of the action and replaced by Ryan Goodfellow with just five minutes on the clock.
Unfazed by the key personnel change, the Pars quickly pushed forward in search of a goal and Callum Morris was not too far away when he nodded just over at the back post from a deep free-kick.
Stephen Husband then had a go with a low drive that was comfortably smothered by Gers goalkeeper Cammy Bell.
On the 18th minute came that backing for King as fans held up their blue cards as a show of support, while chants of 'sack the board' rang out from the stands.
Back on the park, Ross Forbes was booked for diving, before Rangers opened the scoring on the stroke of half-time when Smith dispatched a superb curling free-kick into the top corner from the edge of the 18-yard box.
Rangers swapped Bilel Mohsni for Emilson Cribari for the second half, before McCulloch was withdrawn after an hour, allowing Kyle Hutton to make his first appearance since breaking his leg in November.
The home side were keen to secure the points and Arnold Peralta demonstrated some fine play before attempting to set up Fraser Aird, but the youngster was unable to get the shot away.
The blue cards were out in force again on 72 minutes, before youth player Gallagher was thrown into the action in place of goalscorer Smith two minutes later.
And the youngster was quickly in the thick of it when he was brought down by Danny Grainger on the edge of the box, earning the Pars man his second yellow as he was dismissed with 12 minutes to go.
Rangers were unable to capitalise on the resultant free-kick but Gallagher put the gloss on the victory when he lashed home just before the full-time whistle.