The former Manchester City and Liverpool striker was handed a recall by Mancini - who has previously managed him at club level too - and took just 21 minutes to repay the faith shown in him by the new Italy boss.
Andrea Belotti then doubled Italy's advantage with just over 20 minutes remaining, and the Azzurri, who failed to qualify for this summer's World Cup, held out in St Gallen despite a quick response from Yehya Al Shehri.
Balotelli looked eager to make the most of his return from international exile even before he opened the scoring, laying on a chance for Lorenzo Insigne after just eight minutes which the Napoli man could not take.
Italy were determined to make a quick start to the Mancini era, though, and they came close again with only 14 minutes on the clock when Matteo Politano's corner was nodded wide of the target by Lorenzo Pellegrini.
As is so often the case one way or another, though, Balotelli ensured that the headlines would belong to him midway through the first half when he picked up a loose ball before dipping inside onto his right foot and arrowing a low strike into the bottom corner from 25 yards - his first Italy goal since netting the winner against England at the 2014 World Cup.
Saudi Arabia - who unlike Italy will be at the World Cup this summer - managed to stem the flow of chances as the first half wore on, although they needed the crossbar to come to their rescue with just four minutes remaining until half time when Domenico Criscito's effort came back off the woodwork.
Italy continued to look the more likely to add to the scoring in the second half, and they perhaps should have done 11 minutes after the restart when Pellegrini again failed to make the most of a presentable chance, firing narrowly over from inside the box.
Balotelli's international comeback ended just before the hour mark when he was replaced by Belotti, and the sub made an impact within 10 minutes of his introduction when he fired home a rebound from close range after seeing his initial header saved by the keeper.
Saudi Arabia responded within four minutes to halve the deficit, though, with Al Shehri capitalising on a mistake by Davide Zappacosta before rounding Gianluigi Donnarumma and slotting the ball into the empty net.
Donnarumma pulled off a fine save to avoid further embarrassment for Italy just seven minutes later, denying Fahad Mosaed Al Muwallad Al Harbi from inside the area to keep his side's lead intact.
It proved to be a crucial stop as Saudi Arabia struggled to force any further chances in the closing stages, with Italy coming closest to the game's fourth goal when Bryan Cristante saw his effort blocked in the second minute of injury time.
Italy will next take on France and fellow World Cup absentees Netherlands, while Saudi Arabia will wrap up their preparations for this summer's tournament against Peru and world champions Germany.
ITALY (4-3-3): Donnarumma; Zappacosta, Bonucci, Romagnoli, Criscito (De Sciglio 88'); Florenzi (Bonaventura 67'), Jorginho, Pellegrini (Verdi 73'); Politano (Cristante 73'), Balotelli (Belotti 58'), Insigne (Chiesa 84')
SAUDI ARABIA (4-2-3-1): Al Owais; Al Shahrani, Os Hawsawi (Albulayhi 84'), Om Hasawi (M Hawsawi 94'), Al Hardi; Otayf, Al Faraj (Mogahwi 93'), Al Shehri, Kanoo (Al Dawsari 46'), Al Jassim; Aseri (Al Muwallad 69')