A tight match looked to be heading for a stalemate after Achraf Hakimi had struck the post with the best chance, until Darmian stepped off the bench to secure a first victory in three for Antonio Conte’s side.
Inter now only require a maximum of six more points from their final five games to win the title for the first time since 2010.
A tightly-fought opening period saw Inter come closest as Romelu Lukaku’s flick on released Lautaro Martinez to break clear, but the Argentine’s attempt to lob Marco Silvestri went just over.
Nerazzurri wing-back Hakimi saw a bending effort whistle wide, whilst he drove into the box and forced a fine low save from Silvestri. From the resulting corner, Gianciacomo Magnani almost headed into his own net.
At the other end, Bessa found space in the box and saw his shot blocked by Samir Handanovic, whilst Federico Dimarco’s follow up whistled past the far post with Kevin Lasagna sliding in.
Lasagna pulled a header wide from a Darko Lazovic cross shortly before the interval, as Verona struggled to break through Inter’s resolute defence.
The visitors made a bright start to the second half and as Marco Faraoni saw a header go inches wide from an early corner.
Lukaku almost released Martinez again with some fine hold up play, but the striker was intercepted in the box by Koray Gunter as he shaped to shoot.
Verona were seeing more of the chances in the first quarter of an hour of the second half, but left themselves vulnerable on the counterattack. A quick break saw Martinez charge up field and release Christian Eriksen, but the Dane fired straight at Silvestri.
Inter came within inches of breaking the deadlock with just 20 minutes remaining as Hakimi rifled a freekick against the post, with the Nerazzurri pushing for a winner.
Their pressure told off minutes later as Darmian stepped off the bench to score, with the Parma loanee finding space in the box and tucking the ball under Silvestri after a Hakimi through ball.
The victory sees Inter earn a first win in three matches and move another step closer to the Scudetto.