Australian midfielder Stella was in the right place at the right time to put the hosts ahead in the first half at Ibrox.
He had a quiet game otherwise but contributed to a victory as Gers filled their gap in play due to the international break with a worthwhile friendly.
Ally McCoist fielded an experimental team against the Bairns and deployed his starting line-up in a 3-4-3 formation.
Kamil Wiktorski joined Sebastien Faure and Emilson Cribari in defence, with Lee McCulloch joined in midfield by Robbie Crawford, Artemis Argyriou and Stella.
Kyle spearheaded the attack, with Barrie McKay and latest signing David Templeton either side of him.
There was no sign of Dean Shiels, Andy Little, Chris Hegarty or Andy Mitchell as all four are on international duty with the full and under-21 Northern Ireland teams.
Lee Wallace also sat the game out due to a knock which stopped him from joining the Scotland squad while Ian Black and Fran Sandaza were also missing.
Stella nearly struck inside 70 seconds when he started a move which led to him being in on goal but being beaten to the ball at the last second by the keeper.
Kyle then headed past the post and McKay had a chance to shoot but made the wrong choice when he set up Crawford instead and he missed.
Falkirk got forward well in the first half and Lyle Taylor, their most threatening forward, shot wide as the visitors tried to respond.
He drilled past the post though and that was the cue for Stella to break the deadlock at the other end with a close-range finish from a deep right-wing cross.
Back came Falkirk through Taylor once again and he hit the bar as the Westfield side came close to an equaliser.
Templeton should have made it 2-0 after taking advantage of a defensive lapse to get past the last defender but his effort was straight at the keeper.
And in their next attack the First Division side drew level as substitute Kyle McAusland fouled Taylor in the box and he sent Scott Gallacher the wrong way from the spot.
Rangers rallied and eventually went in front once more with 19 minutes of the match remaining.
Replacement Kal Naismith did really well to break away from two opponents before playing the ball to Kyle on the 18-yard line.
He then flicked the ball on to Tom Walsh, whose shot was screwing across goal and wide until it deflected off a defender and into the net instead.
Fraser Aird could have added a third late on with a rasping drive from 30 yards but it was stopped on the line.
And instead it was Kyle who sealed the victory seconds from the end when he nodded in a Walsh cross at the back post after a short corner from Naismith.
McCoist will have been pleased the forward, along with Faure, Crawford and Hutton, got valuable minutes under their belts.
He’ll also have been happy McAusland came through his return from a hip injury unscathed and that youngsters Walsh, Murdoch and Naismith showed up relatively well.
RANGERS (3-4-3): Gallacher; Wiktorski (Murdoch), Faure, Emilson (Pascazio); Argyriou (McAusland), McCulloch (Hutton), Crawford (Aird), Stella; McKay (Walsh), Kyle, Templeton (Naismith).