The Brazilian headed Michael Beale’s side in front early in the match, before substitute Matondo doubled the advantage in the second-half.
The manager named six changes to his side from the last Scottish Premiership fixture two weeks ago as Ben Davies, Ridvan, John Lundstram, Tom Lawrence, Sam Lammers and Danilo all came into the starting XI.
That meant Rangers started in Perth with Jack Butland in goal and a back four of James Tavernier, Connor Goldson, Ben Davies and Ridvan.
Nico Raskin retained his place in midfield and was joined there by John Lundstram and Tom Lawrence while Sam Lammers, Kemar Roofe and Danilo provided the attack.
It was Rangers who got the action underway as Beale’s men looked to get back to winning ways in the league against the Perth side.
The Light Blues dominated possession in the opening stages of this match as they searched for an early breakthrough. Kemar Roofe came the closest in that period with a strike from a narrow angle which was just wide of Mitov’s right-hand post.
The early dominance paid off though and, with 16 minutes on the clock, Rangers were ahead as Danilo found the target with a header. It was a good move from Rangers as from a St Johnstone corner the Light Blues broke up the pitch with Sam Lammers finding captain James Tavernier who had made a darting run forward.
Tavernier took a touch beyond Luke Robinson before whipping a lovely ball into the box which Danilo managed to get his head on to guide beyond Mitov and give Rangers the lead.
It was a bittersweet moment for the Brazilian who collided with St Johnstone captain Liam Gordon as he headed the ball home, with both players requiring treatment in the area with both players unable to carry on.
Abdallah Sima was introduced in place of the striker and almost had a goal in his first few minutes on the pitch with a low drilled effort which was blocked by the feet of Mitov.
As the game approached half-time, Sima came close again as he did well to link-up with Kemar Roofe and John Lundstram before getting a shot away at goal but the forward’s attempt was held by Mitov.
Kemar Roofe sent a header just over the bar as he got on the end of a Ridvan cross as Michael Beale’s side pushed for a second-goal before the break.
Before the break, St Johnstone had an opportunity from a set-piece as they were awarded a free-kick around 25 yards out. Graham Carey lifted the ball over the top and into the path of Max Kucheraivyi but his shot was held comfortably by Butland, who had had a quiet afternoon so far in the Rangers goal.
The home side came out in the second-half looking to cause Rangers some problems as they searched for a route back into the game. A good delivery from Graham Carey drifted across the Rangers goal in search of Chris Kane at the back post but he was unable to connect with the ball.
Oludare Olufunwa had an opportunity for Steven as he curled a shot towards goal but Ben Davies was able to head the shot wide to deny the home side.
Kemar Roofe had the ball in the back of the net with 25 minutes of the match remaining as he touched home from inside the area but after a VAR check, referee Nick Walsh disallowed the goal for offside from Abdallah Sima in the build-up.
Connor Goldson fired just over the bar from a James Tavernier corner shortly after as Rangers continued to search for that second goal.
Beale turned to his bench on the 73rd minute as Rabbi Matondo was introduced in place of Sam Lammers for the final period in Perth.
Just minutes after coming on, Matondo picked out the run of Tom Lawrence as he drove towards goal but his strike from inside the box was gathered by Mitov.
Matondo had made a positive impact and just five minutes after his introduction he found the target with his first league goal of the season. It was a fantastic goal from Rangers as Nico Raskin and Tom Lawrence broke through the St Johnstone defence before the latter played in Matondo.
The Welshman, who cut into the box and showed composure to curl a right-footed shot into the back of the net.
The goal ensured the remaining period was comfortable for Beale’s men with Sima and Matondo both having chances in the final stages.
Rangers: Butland, Tavernier, Goldson, Davies, Ridvan, Raskin, Lundstram, Lawrence, Lammers (Matondo, 73), Danilo (Sima, 19), Roofe.
Subs: McCrorie, Souttar, Jack, Dessers, Cifuentes, Sterling, Barisic.
St Johnstone: Mitov, Considine, Gordon (McClelland, 20), Kane (Turner-Cooke, 80), Carey, Kucheraivyi (May, 70), Olufunwa, Robinson, Smith, Phillips (MacPherson, 80), Costelloe.
Subs: Richards, Brown, Gallacher, Jephcott, Franczak.