Danny Röhl’s side found themselves 2-1 down with just 30 minutes played after Marc Leonard and Claudio Braga had scored for the visitors and Michael Steinwender had also put the ball into his own net.
The Light Blues needed someone to step up to the plate and Chermiti was the man to do just that as he struck in the 39th, 57th and 90th minutes to complete a remarkable man of the match display.
After Wednesday’s 1-1 draw at Fir Park, this was the perfect way for Rangers to bounce back and although it was far from straightforward, the work-rate and desire from the players in blue was there for all to see.
Personnel from the Royal Marines abseiled into the stadium from the Broomloan, Copland and Sandy Jardine Stands - delivering the match ball to referee Don Robertson – and it was Nico Raskin who got the game underway from the kick-off in front of a fired-up home support, with 160 special guests from the Army, Royal Navy and RAF in attendance.
With just three minutes on the clock, however, Eduardo Ageu showed a bit too much passion and enthusiasm for the visitors, with his late, sliding challenge on Raskin inside the centre circle producing the first yellow card of the match.
Derek McInnes was then forced to make his first change to his team, with Steinwender replacing the injured Oisin McEntee, who appeared to be clutching his shoulder as he walked up the tunnel.
It was an eventful opening to the match and, on 16 minutes, the drama really started as Hearts made the most of a defensive error to score the first goal of the game.
A slack pass from Emmanuel Fernandez to Raskin was intercepted by Marc Leonard who fed the ball to Claudio Braga in the box.
Instead of shooting, the number 10 played it back to Leonard who, from around 14 yards, produced a powerful yet composed finish which flew past Jack Butland, giving the goalkeeper no chance.
The Rangers fans demanded a quick response from their team and just three minutes later they were back on level terms.
It all started from positive play from the energetic Tuur Rommens; the left-back getting into a great attacking position and delivering a pinpoint cross. Chermiti rose to meet it and Alexander
Schwolow palmed his header away brilliantly.
Following the save, the ball fell to Mikey Moore who – from eights yards out - blasted a shot off the ground and up onto the underside of the crossbar. When it dropped back down, substitute Steinwender’s sclaffed clearance from close range flew into the net and Ibrox erupted.
Their joy was to be short-lived though as Hearts got their noses back in front on the half-hour mark. A cross from the right from Steinwender was perfect for Braga who, at full stretch and with John Souttar challenging him, somehow managed to angle a terrific, looping header past Butland at his far post.
This frenetic first half of football was not over yet as Rangers once again found an equaliser, with Chermiti getting his first of the day on 39 minutes.
The Portuguese striker received the ball in the right channel of the Jambos’ 18-yard box from Ryan Naderi and he got a bit of luck, with his initial shot hitting the sliding Craig Halkett and returning to him so he had a second attempt.
He made the most of that good fortune though as he powered a low shot into the net in front of a jubilant Broomloan Stand.
McInnes made two further changes to his side for the start of the second half, with Ageu and Islam Chesnokov replaced by Pierre Landry Kabore and Jordi Altena.
Röhl, at this point, stuck with the same eleven and in the 57th minute the Gers fans were out of their seats again celebrating their team’s third goal of what was quickly becoming an unforgettable afternoon.
Skov Olsen was the provider of the assist, the Dane finding acres of space on the right wing to take a touch and deliver a whipped cross to the near post area. Chermiti was again in the right place at the right time to send a majestic, glancing header into the roof of the net.
The noise in the stadium was now deafening, the Ibrox faithful fully appreciating their players’ efforts and desire to take the lead against the league leaders, who themselves were throwing everything into this crucial league clash.
With James Tavernier introduced from the bench just after Chermiti’s second goal, the Light Blues now had a slender advantage to protect and the icing on the cake came in the 90th minute.
Substitute Djeidi Gassama darted forward and found Chermiti in space. With his confidence high the big forward made no mistake, sweeping a fine finish low into the net before celebrating in style.
RANGERS: Butland, Sterling (Tavernier 57), Souttar, Fernandez, Rommens, Raskin, Chukwuani, Skov Olsen (Diomande 80), Moore (Gassama 88), Naderi (Antman 80), Chermiti
SUBS NOT USED: Kelly, Meghoma, Djiga, Aasgaard, Antman, Miovski
GOALS: Steinwender 19og, Chermiti 39, 57, 90
BOOKINGS: Skov Olsen, Chermiti, Gassama
HEARTS: Schwolow, Halkett, Baningime (Magnusson 74), Braga, Milne, Findlay, McEntee (Steinwender 12), Ageu (Kabore 45), Leonard, Kyziridis, Chesnokov (Altena 45)
SUBS NOT USED: Gordon Kent, McCart, Spittal, Mato
GOALS: Leonard 16, Braga 30
BOOKINGS: Ageu, Leonard, Milne
REF: Don Robertson