Bonatini, who has joined Wolves on a season-long loan from the Saudi Arabian side Al Hilal, pounced on a 33rd-minute mistake in the Middlesbrough defence.
The goal also ensured that it was the perfect start for new Wolves manager Nuno Espirito Santo in front of sold-out Molineux.
But it was not the beginning to his reign that new Middlesbrough chief Garry Monk had been seeking after his expensive outlay on new players.
With 13 debutants on show - seven from Wolves and six from Middlesbrough - it was perhaps not surprising that the opening stages of the game saw the two new-look teams struggle to create any real chances of note.
Adam Clayton's 14th-minute free-kick, after George Friend had been fouled by Wolves right-back Matt Doherty, did cause concern in the hosts penalty area until it was steered behind for a corner by Bonatini.
While Middlesbrough toiled for an opening, Wolves were equally short of success in front of goal.
Bonatini did do well to tee-up £15m club record signing Ruben Neves on the edge of the area in the 19th minute.
But the Portugal international midfielder, who joined Wolves from Porto, was unable to get any power on his shot and it was comfortably cleared by the Middlesbrough backline.
It looked like it would need something inspired or a mistake to end the stalemate and unfortunately for Middlesbrough it was a howler from Daniel Ayala that let in Bonatini to break the deadlock and finally spark the game into life.
A misplaced pass by Ayala was intercepted by Bonatini and he strode into the penalty area before rolling the ball past the stranded Middlesbrough goalkeeper Darren Randolph.
But Wolves advantage should really have been short-lived as Martin Braithwaite squandered a golden opportunity to equalise two minutes before the interval.
Cyrus Christie delivered an excellent right-wing cross that picked out Braithwaite only for the Danish forward to lift his header well wide after coming under pressure from goalkeeper John Ruddy.
Having wasted that opening, Middlesbrough were fortunate not to fall further behind six minutes after the restart when only the outstretched hand of Randolph prevented Bright Enobakhare from doubling Wolves advantage after a powerful run into the penalty area.
Converting that chance would have eased Wolves nerves as Middlesbrough looked for a way back on to level terms.
They would have found an equaliser in the 72nd minute had it not been for Ruddy.
Middlesbrough's £15m striker Britt Assombalonga was set-up by Patrick Bamford only for Ruddy to spread his body to beat away the close range shot.