But it was Denzel Dumfries who decided the game with a stoppage-time winner to see Inter snatch a 2-1 victory at newly-promoted Lecce on Saturday, just as the Nerazzurri appeared to be heading for a surprise draw.
"It's a victory that we wanted with our hearts, the team believed right until the end," Inter coach Simone Inzaghi said.
"Objectively though, a team like ours should have finished it off earlier, especially as we scored in the first minute.
"We had a great spirit but we have to analyze why we were reduced to wining at the last second."
AC Milan also got off to a winning start as it opened its defense of the league title with a 4-2 truimph over Udinese — albeit with the help of a controversial penalty.
Inter brought back Lukaku on loan this offseason, a year after he left to join Chelsea shortly after firing the Nerazzurri to the Serie A title.
Coincidentally, Lukaku kicked off his second stint at Inter at the same team he faced on his first debut when he scored in a 4-0 win three years ago.
And it took the Belgium forward less than two minutes to reopen his Inter account. Federico Dimarco floated in a cross from the left and Matteo Darmian nodded it back across goal for Lukaku to head in from close range.
Unlike in Lukaku's first debut, however, there was to be no capitulation from Lecce. And the home side levelled shortly after the break when Federico Di Francesco fed Assan Ceesay for an angled drive into the far bottom corner.
Lecce almost took a surprise lead on the hour mark but Inter goalkeeper Samir Handanovic did well to parry Kristijan Bistrovic's fierce free kick.
It was all Inter after that, though. Dumfries saw a header come off the post, while Lukaku had a goal ruled out for a foul in the buildup.
Lecce goalkeeper Wladimiro Falcone also pulled off a number of impressive saves, including denying Lukaku late on.
But Falcone was let down by his defenders in the fifth minute of stoppage time as they failed to mark Dumfries and he chested the ball in from point-blank range after Lautaro Martínez had nodded down a corner.
It took less than 10 minutes of the Serie A season for the first refereeing controversy to arrive.
Milan was trailing when captain Davide Calabria collided with opposing defender Brandon Soppy as both went for the ball in the penalty area.
After a lengthy pause while he reviewed the incident on the pitchside monitor, referee Livio Marinelli awarded a penalty to Milan — much to the outrage of the visiting team.
Theo Hernández converted the penalty and Ante Rebic volleyed Milan in front shortly afterwards.
Udinese was one of the only teams — along with Juventus — Milan had failed to beat in its title-winning campaign.
And a sold-out San Siro was silenced with less than two minutes on the clock when Rodrigo Becão headed in a corner to give Udinese a shock lead.
Although Milan swiftly turned things around, it found itself pegged back at the break when Roberto Pereyra floated in a cross from the right and Adam Masina got away from his marker for a diving header on the stroke of halftime.
However, Milan restored its lead just 30 seconds after the interval as two Udinese defenders got into a tangle as they tried to deal with Hernández's cross, allowing Brahim Díaz to tap in at the back post.
Díaz also had a hand in Milan's fourth as he muscled his way along the byline before rolling the ball across for Rebic to fire into the top left corner.
Two of Milan's new signings made their debut as Belgian players Charles De Ketelaere and Divock Origi were brought on in the second half.
The 21-year-old De Ketelaere had a late goal ruled out for offside.
Silvio Berlusconi's return to Serie A ended in defeat as his newly-promoted Monza side lost 2-1 at home to Torino.
Berlusconi had owned Milan for 31 years before selling in 2017. The former Italy premier bought Monza the following year.
Meanwhile, substitute Ademola Lookman scored on his debut to help Atalanta win 2-0 at Sampdoria. Lookman's goal came in stoppage time after Samp had hit the woodwork twice.
Rafael Tolói had scored Atalanta's opener.