Philippe Clement was seeking a response from his Gers side, who failed to win each of their previous three Scottish Premiership matches, including a 3-2 defeat at Ross County and a drab goalless stalemate with Dundee on Wednesday.
The Belgian boss relied on Cyriel Dessers to fire his side to victory over a spirited Hearts outfit, with the striker on target in either half to ensure Rangers' keep their hopes of winning a domestic treble alive.
Rangers, who also beat Steven Naismith's side 3-1 en route to lifting the Scottish League Cup earlier this season, can now look forward to an Old Firm final in the Scottish Cup back at the national stadium on May 25.
Holders Celtic edged past Aberdeen 6-5 on penalties in Saturday's semi-final following an enthralling 3-3 draw in 120 minutes, sending them through to their 60th Scottish Cup final.
Dessers delivers for Rangers with brace
Rangers made a bright start to the contest and put themselves ahead inside the opening five minutes when Dessers fired a low left-footed strike past Craig Gordon from inside the box after Hearts failed to clear their lines - credit should go to James Tavernier for winning the second ball to begin the attack.
The Jam Tarts were at sixes and sevens at the back and initially struggled to deal with the link-up play between Todd Cantwell and his fellow attackers, although one of those - Abdallah Sima - was forced to make way on the 15-minute mark due to injury.
Hearts gradually grew into the game and Rangers had goalkeeper Jack Butland to thank for making two saves in the space of a minute, firstly keeping out Alan Forrest at his near post before denying Frankie Kent with a magnificent instinctive stop from point-blank range.
Rangers looked a yard sharper than their Edinburgh-based counterparts in the early stages of the second half, with Cantwell continuing to pose a threat in central areas in the final third, but it was Hearts who were presented with the first big chance after the break.
John Souttar, formerly of Hearts, dawdled in possession and had the ball nicked off him by Kenneth Vargas down the right, but he delayed his pass into the danger zone and Tavernier was alert to intercept and clear.
Just two minutes later, Souttar redeemed himself with a crucial block to deny Lawrence Shankland at the near post before John Lundstram scrambled the ball away to safety.
Hearts fans were beginning to believe for the first time in the contest as they watched their side put Rangers under a fair amount of pressure. In search of an equaliser and a fresh urgency in attack, Naismith made a triple substitution, with Barrie McKay, Dexter Lembikisa and Yutaro Oda all thrown into the action for the final half-hour.
The closely-fought contest soon became stretched, with Dujon Sterling and Dessers both posing a threat before Shankland thought he had restored parity for Hearts, only to see his header from a tight angle at the far post crash into the side netting.
Hearts' efforts to net a leveller were ultimately in vain as Dessers sealed the victory for Rangers in the 78th minute, converting at the second time of asking after receiving a pass from Cantwell, who began the counter-attack with a brilliant mazy run towards the penalty area.
Butland then pulled off another exceptional save in the closing stages, this time diving at full stretch to his right to keep out a strike from Oda, and Rangers eventually saw out a nervy final few minutes to secure their spot in the showpiece event.
Rangers set up historic finale to keep domestic treble hopes alive
Victory for Rangers keeps them on course to end the campaign with a domestic treble; having already lifted the Scottish League Cup, the Gers are only 90 minutes away from Scottish Cup glory and they also remain in the Premiership title race along with arch rivals Celtic.
Rangers will soon meet Celtic in the Scottish Cup final for the 14th time in their history, but remarkably for the first time since 2001-02 when they beat the Hoops 3-2 under former boss Alex McLeish.
Since then, Rangers have reached five Scottish Cup finals and have won four of those, including their most recent against Hearts in 2021-22 - their 34th triumph in the competition.
Celtic, meanwhile, have won each of their last 10 appearances in the Scottish Cup final since losing to their Old Firm foes 22 years ago, winning five of the competition's last seven finals to take their record tally of triumphs to 41.
Rangers will now turn their attention back to the Premiership with a trip to Paisley to face St Mirren next Sunday.