The midfielder scored the only goal of the game to continue Clarence Seedorf side's recent run of form
In what has been a largely disappointing campaign so far for the Rossoneri, there may yet be light at the end of the tunnel as their end-of-season resurgence under Clarence Seedorf continued at San Siro on Sunday.
Their latest victory has taken them to within five points of rivals Inter, who occupy the last guaranteed Europa League spot, although sixth place could also still provide a berth in Europe's secondary competition should Coppa Italia finalists Napoli and Fiorentina finish in the top five.
Meanwhile, defeat for Maurizio Pellegrino on his second debut as Catania head coach means his side are now eight points adrift of safety with just five matches to play.
Montolivo, who netted in Milan's 3-1 victory at Catania earlier this season, scored the game's only goal in the 23rd minute thanks to a superb long-range effort.
And while a second goal proved elusive, Milan controlled the match and were aided by Fabian Rinaudo's late red card following an over-the-ball lunge on Philippe Mexes that resulted in a second booking.
Catania started life under Pellegrino brightly, with winger Pablo Barrientos flashing a shot across goal, and he continued to be at the heart of their attacking forays, forcing a fine one-handed save from Milan goalkeeper Christian Abbiati.
Barrientos' curling 25-yard effort awoke Milan from their slumber and Adil Rami went close to giving them the lead, flicking Kaka's whipped free-kick from the left over the bar.
Montolivo then produced his moment of brilliance, striking a 25-yard drive that arrowed into the bottom left-hand corner.
The goal appeared to galvanise Milan, who started to look more assured in possession, and Adel Taarabt bent a 20-yard effort just wide shortly after the half-hour mark.
Mario Balotelli was next to go close, curling a free-kick narrowly past the left-hand post, and Milan continued to dictate the tempo in the second half.
Balotelli could have doubled their lead, only for team-mate Andrea Poli to take the ball away from him following Taarabt's dangerous cross.
Defender Mexes almost scored an outrageous goal, with the centre-back's acrobatic scissor-kick going over from Balotelli's dinked free-kick, and Nigel De Jong was then denied by Catania goalkeeper Mariano Andujar.
Milan could not find the all-important second goal but the visitor's hopes of salvaging a draw were dealt a blow with 11 minutes left as Rinaudo was given his marching orders.
Taarabt then curled wide again before Balotelli shot over, but one goal would prove enough for Milan as they posted four league wins in a row for the first time since March 2013.