AC Milan finished fifth last season, missing out on Champions League qualification, but have changed coaches with former Sampdoria boss Marco Giampaolo taking over from Gennaro Gattuso.
The seven-time European champions were lacking inspiration in Udine, though, without a single shot on target against a Udinese side who finished 12th last term after fighting to avoid relegation.
The breakthrough came after 72 minutes when 23-year-old Becao connected with a Rodrigo De Paul corner to head past Gianluigi Donnarumma in the Milan goal.
Donnarumma got his fingers to the ball to prevent a second from Kevin Lasagna just minutes later.
Cancer-stricken Mihajlovic on bench
Bologna coach Sinisa Mihajlovic left the hospital where he was being treated for leukemia on Sunday to take charge of his team for their opening Serie A match away to Verona.
The club announced before kickoff that the 50-year-old, who said on July 13 that he had a severe form of the illness but promised to win the battle, would "leave the hospital to lead the team at Verona."
It was a personal victory for the Serb, but the match ended 1-1 with Bologna settling for a point despite promoted Verona finishing the game with ten men.
Bologna went ahead in the 15th minute when Nicola Sansone converted a penalty which also left promoted Verona down to 10 men as Pawel Dawidowicz was sent off for the foul on Riccardo Orsolini.
A cap on his head and wearing a Bologna shirt, coach Sinisa Mihajlovic courageously joins his players for their Serie A opener in Verona on Sunday despite undergoing treatment for leukemia. /VCG Photo
Bologna appeared to be in control until Miguel Veloso equalized out of the blue from a free kick in the 37th minute.
Mihajlovic, one of the sport's top free-kick exponents during his playing days, took over at Bologna halfway through the last season with the team stuck in the relegation zone and performed a remarkable transformation as he led them to a 10th place finish.
"We were shocked, we didn't expect it, even though he had promised us," midfielder Andrea Poli told sports broadcaster DAZN.
"We were impressed, but we are happy that he is here with us, he shows exceptional courage. We were excited when he arrived at the hotel."
Serie A results:
Udinese 1-0 AC Milan
Verona 1-1 Bologna
Cagliari 0-1 Brescia
Roma 3-3 Genoa
Sampdoria 0-3 Lazio
SPAL 2-3 Atalanta
Torino 2-1 Sassuolo
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