After Gerard Deulofeu had given Udinese an early advantage, Osimhen equalized after the break with a header then won it with one-touch by redirecting a cross from Giovanni Di Lorenzo.
Oshimhen, who also had a brace in Napoli’s 2-1 win at Hellas Verona last weekend, will miss the team’s next match for accumulated cards.
Udinese was reduced to 10 men in the end when Pablo Mari was sent off with a straight red for a high foul on Piotr Zielinski.
Amid a tight race for the Serie A title, AC Milan is displaying more consistency than its rivals.
AC Milan wins 1-0 at Cagliari
On a night when defending champion Inter Milan was held to a 1-1 draw at home by Fiorentina, Milan won 1-0 at relegation-threatened Cagliari to extend its unbeaten run to eight matches.
Milan remained three points ahead of Napoli, which came from a goal down to beat visiting Udinese 2-1 earlier Saturday.
On a rainy night in Sardinia, Ismael Bennacer scored with a long-distance volley for Milan near the hour mark. The goal was set up by Olivier Giroud, who failed to take advantage of a prime opportunity early on when he missed the target from close range.
Also in the first half, Milan midfielder Franck Kessie hit the post from long range.
Cagliari nearly equalized in the 90th with a shot from Leonardo Pavoletti that hit the crossbar.
Milan won at Napoli two weeks ago, while Inter has gained only seven points from its last seven matches.
Torreira scores, looses tooth
Third-place Inter lost ground in the title race after being held to a 1-1 draw by Fiorentina at the San Siro.
The defending champion won just one of its last seven games. The Nerazzurri trail Milan by six points but have a game in hand.
Lucas Torreira put Fiorentina ahead after the break after beating Nicolo Barella to a cross.
Denzel Dumfries equalized for Inter five minutes later with a header.
Torreira, who is on loan from Arsenal, played on despite losing a tooth in the match. The Uruguay international also scored in Fiorentina’s previous match.
Fiorentina is eighth.
AP