A goal from Andrew Little was enough for Rangers to knock holders Falkirk out of the Ramsdens Cup.
The Northern Irish forward tucked away a shot on the stroke of half-time to settle a close contest.
It was Little's sixth goal of the season and he picked his spot in the bottom corner after good set-up play from Francisco Sandaza.
Falkirk enjoyed good spells of possession but did not pose enough threat in the final third.
The win allowed Rangers to take their revenge on the Bairns, who dumped Ally McCoist's men out of the Scottish Communities League Cup last season - with the two sides set to meet again in that competition at Ibrox next week.
In-form Little almost opened the scoring early on when he raced on to a Kirk Broadfoot pass, only to see his close-range shot blocked by goalkeeper Michael McGovern.
Falkirk had a chance of their own when David Weatherston squared across the face of goal for the onrushing Lyle Taylor, but he just failed to connect at full stretch.
Rangers were threatening when Ian Black curled a free-kick into the box and Sandaza rose above everyone else in the packed goalmouth, only to nod wide.
The breakthrough came when Little collected from Sandaza before driving low past McGovern from a tight angle.
Falkirk set about trying to haul themselves back into the tie after the break and Stephen Kingsley picked out Kieran Duffie at the back post, but he fired straight into the hands of goalkeeper Neil Alexander.
Rangers, who were missing the injured Lee Wallace and Dean Shiels, then made a double switch when Kevin Kyle and Kal Naismith were thrown into the action for Barrie McKay and Sandaza.
The visitors tried to end any hopes of a late Falkirk fightback and a shot from Lewis McLeod was hooked off the line by Blair Alston
Rangers held on to claim a narrow victory and ensure their names will be in Wednesday's draw for the quarter-finals.
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