Danny Rohl's side trailed to goals from Ben Broggio and Finn Yeats in a shambolic first-half performance.
But Tochi Chukwuani gave Rangers hope with a controversial goal just before the interval.
Three goals in 11 minutes early in the second half turned the tide in Rangers' favour.
Youssef Chermiti equalised and Nicolas Raskin put Rangers ahead before Bojan Miovski grabbed the visitors' fourth.
Calvin Miller's penalty couldn't rattle Rangers as Chermiti and Miovski struck again to seal the points.
Wins for Hearts and Celtic on Saturday had put the onus on Rangers to keep pace with their title rivals.
Rangers responded, leaving them just one point behind leaders Hearts and two ahead of third-placed Celtic as the title race approaches a thrilling finale.
Rangers haven't won the title since 2021, while Hearts are aiming to dethrone champions Celtic by taking their first Scottish crown since 1960.
Rangers' raucous victory was a far cry from their last visit to Falkirk in October.
That 1-1 draw was the final game of Russell Martin's dismal reign, with the manager needing a police escort to protect him from angry fans.
Rangers have been revitalised by Rohl, but it was hard to discern that impact when Falkirk went ahead after just six minutes.
Miller whipped a low cross towards Broggio, who easily evaded Rangers' sloppy marking to slot home from six yards.
Falkirk doubled their lead in the 26th minute as Yeats rifled a powerful strike past Jack Butland from the edge of the area.
Chukwuani reduced the deficit in bizarre fashion in the 42nd minute.
He prodded home from five yards after Falkirk stopped in a mistaken belief that a cross had gone out of play before it was headed onto the post and rebounded to the Rangers goal-scorer.
VAR checked the incident, but Chukwuani was eventually able to celebrate after the replays proved inconclusive.
Chermiti hauled Rangers level with a simple finish from Djeidi Gassama's 47th-minute cross.
Rangers' stirring comeback was complete five minutes later.
Raskin took possession 20 yards from goal and smashed a fine finish into the far corner before jumping into the stands to celebrate, in the process banging his head on one jubilant Rangers supporter.
It wasn't enough to force him off and Raskin played a key role when Rangers' blistering spell produced a fourth goal in the 58th minute.
Miovski bundled Raskin's pinpoint cross into the net from close range.
Miller fired home from the penalty spot in the 70th minute after James Tavernier fouled Filip Lissah.
But Chermiti eased Rangers' anxiety four minutes later with a thunderous blast from the edge of the area, and Miovski tapped in the sixth in the 88th minute.