The Brazil striker had not scored since his two strikes against Siena in the Serie A opener but he handed the struggling Rossoneri all three points.
Jeremy Menez gave Roma a third-minute lead before Ronaldinho equalised shortly after the re-start.
Pato then made the most of a wonderful pass from Ronaldinho in the 67th minute to put the hosts in front for good.
Milan were forced to play the last eight minutes of the game with 10 men after captain Massimo Ambrosini was shown a second yellow card for a foul on Nicolas Burdisso but held on for their third victory to climb to eighth in the standings.
No victory has tasted as sweet as this one for Milan's rookie coach Leonardo, who went into the game under pressure with his team having mustered just two points in the last three games.
The home side suffered a blow before the game with goalkeeper Marco Storari ruled out because of flu but veteran Dida proved to be a sturdy replacement.
With Roma's top scorer Francesco Totti unavailable because of a knee injury, Roma coach Claudio Ranieri played with Mirko Vucinic up front and they took an early lead when Thiago Silva's back-pass was intercepted by Menez. He made no mistake and fired past Dida.
Milan first tested Roma goalkeeper Alexander Doni in the 14th minute with Andrea Pirlo's free-kick forcing the keeper to punch away.
Midway through the first half, Daniele De Rossi tried his luck from long range and his powerful effort forced Dida to fully stretch to turn the ball out for a corner.
At the other end, John Arne Riise did well to anticipate Ronaldinho's pass towards Pato as Milan began to come into the game.
Roma should have doubled their lead in the 38th minute after a fast counter-attack left Vucinic with only Dida to beat but his close-range effort was met by a fine save by the keeper.
The hosts almost equalised before the break with Roma's defence failing to clear the ball inside the area. Clarence Seedorf's effort hit the post, though.
Leonardo made one substitution at the interval with Filippo Inzaghi replacing Ignazio Abate.
The replacement almost made an immediate impact, latching onto a corner and heading past Doni only for David Pizarro to make a goalline clearance.
At the other end, Menez surged into the area and fired in an effort which was saved by Dida.
In the 55th minute, the referee pointed to the spot after Burdisso brought down Alessandro Nesta inside the area. Ronaldinho sent Doni the wrong way to level the score.
On the hour mark, Dida was forced to make a desperate clearance with his foot from Riise's powerful free-kick.
Pato then latched on to Ronaldinho's pass and got past Doni before firing into the back of the net.
Roma should have pulled level soon after but Riise failed to find the finishing touch inside the box after Simone Perrotta had tested Dida seconds earlier.
Playing with a numerical superiority, Roma surged forward and enjoyed two good chances.
Substitute Julio Baptista's free-kick went high over the bar while shortly after, Stefano Guberti's diagonal strike from inside the area forced Dida to make a save.
MILAN: Dida; Oddo, Nesta, Thiago Silva, Zambrotta; Abate, Pirlo, Ambrosini, Seedorf; Pato, Ronaldinho.
ROMA: Doni; Cassetti, Mexes, Burdisso, Riise; Taddei, De Rossi, Pizzarro, Perrotta; Menez, Vucinic
