Messias even overshadowed Zlatan Ibrahimovic, who scored Milan's opener.
Milan moved a point below Serie A leaders Napoli, who let slip a two-goal lead to draw 2-2 at Sassuolo.
After losing back-to-back league matches, AC Milan got off to a poor start as Simon Kjaer was injured almost immediately and had to be taken off on a stretcher in the third minute with a knee injury.
But Ibrahimovic curled in a free kick in the 10th minute for his sixth goal in nine league matches.
Messias had scored his first goal for Milan last week in the Champions League to secure a 1-0 win at Atletico Madrid. And he opened his league account with the Rossoneri in first-half stoppage time with a looping header.
The Brazilian, who began his professional career only a few years ago, scored his third goal in a week in the 61st with an angled drive into the bottom left corner.
After leading 2-0, Napoli nearly had to return home without even a point.
Gregoire Defrel celebrated wildly after thinking he had scored a stoppage-time winner for Sassuolo but it was disallowed on video review for a foul by Domenico Berardi in the buildup.
Napoli took the lead with goals from Fabian Ruiz and Dries Mertens. But Gianluca Scamacca pulled one back for the home side and Gian Marco Ferrari leveled in the final minute.
Napoli coach Luciano Spalletti was sent off for dissent immediately after the equalizer.
Lautaro Martinez scored one goal and set up another as Inter Milan beat Spezia 2-0 to close the gap on Napoli.
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