- Romelu Lukaku (20' Pen)
- Henrikh Mkhitaryan (73')
- Lautaro Martínez (89')
- Sandi Lovric (43')
Second-placed Inter, who missed out on their fourth competitive win in a row on Monday when they were held to a goalless draw at Sampdoria, remain a whopping 15 points behind leaders Napoli. They are three points clear of AC Milan in third.
Lukaku gave Inter the lead through a retaken penalty in the 20th minute after the hosts were awarded a spot-kick for a foul on Denzel Dumfries following a lengthy VAR check.
The Belgium striker saw his first take saved by Udinese goalkeeper Marco Silvestri but made no mistake the second time, sending the ball into the low right corner after the referee ordered a retake as the goalkeeper was off the goal line.
It was the 29-year-old's second Serie A goal of the season, coming six months after he was last on target back in August against Lecce.
Udinese equalised with their first shot on target in the match, with midfielder Sandi Lovric firing in just under the crossbar.
As the game continued to be a tight contest after the break, midfielder Mkhitaryan could have restored the lead for Inter in the 65th minute but Silvestri pulled off a great save.
Seven minutes later the Udinese goalkeeper denied Edin Dzeko in a similar fashion.
But he was beaten in the 73rd minute when Federico Dimarco set up Mkhitaryan inside the box for the Armenian to make it 2-1 with his first touch.
Substitute Martinez, who came on to replace Lukaku midway through the second half, tried to lob the goalkeeper in the dying minutes only to send the ball over the bar, before sealing the win one minute from time with an individual effort.
"Playing against Udinese is always difficult, and we already saw that in the first leg," Mkhitaryan told Sky Sport, referring to Udinese's win in the reverse fixture by the same score in September.
"[Tonight] before going ahead, we could have conceded a goal but we were lucky. At 2-1, it was already clear that we would win.
"We are a very strong team, we have shown the whole world that we are not to be messed with."
Inter, who on Wednesday face Porto in the first leg of their round of 16 clash in the Champions League, next travel to Bologna on Feb. 26.
- Federico Dionisi