Roberto Mancini's side finally got back to winning ways on the road but a second-half penalty save from the Slovenian proved vital before a late own goal
Coach Roberto Mancini had warned in the week that "simply being Inter" was not enough to ensure success and that his side would need to put in more effort than their opponents to reap the rewards.
And the former Manchester City boss could have few complaints on Saturday, as a bright start in each half yielded two unanswered goals.
Inter's first came courtesy of Mauro Icardi – returning from suspension – although Verona felt play should have been halted for an injury to Panagiotis Tachtsidis on the edge of the box.
Verona pushed for a leveller but lacked quality in the final third, and Rodrigo Palacio finished from close range three minutes into the second half to give Mancini's side breathing space.
Luca Toni saw a late penalty saved by Samir Handanovic - who has kept out six of the last seven spot-kicks he has faced in Serie A - and Verona's evening went from bad to worse when Vangelis Moras scored an own goal in stoppage-time.
Victory for Inter moved them above AC Milan and Genoa into eighth, although their city rivals are yet to play this weekend.
Inter started the match visibly determined to end their disappointing run, and Fredy Guarin felt he should have been awarded a free-kick on the edge of the box when he went down under the challenge of Jacopo Sala in the opening few minutes.
The visitors continued to press and their 11th-minute opener came in controversial circumstances.
A Tachtsidis slip in the build-up had left the midfielder stricken on the edge of the box, but Inter played on and Palacio's cross deflected off Eros Pisano into the path of Icardi, who applied a simple finish.
Verona were enraged but despite growing into the game as the half progressed, they failed to really test Inter goalkeeper Handanovic.
Inter could easily have been two up at half-time, but Marcelo Brozovic pulled wide of the left-hand post after being played in by Palacio.
It did not take long for Mancini's men to make amends after the interval, though, as an incisive counterattack ended with Palacio poking home from an Icardi cross.
Mounir Obbadi unleashed a shot that squirmed through a host of Inter defenders to be punched away by Handanovic, who then rose to his feet to deny Moras seconds later.
With time running out, Verona saw penalty appeals for an alleged Nemanja Vidic handball turned down, before Palacio missed a chance to put the result beyond doubt when he struck a post at the other end.
That squandered opportunity looked set to be punished when Verona were awarded a penalty with 14 minutes left to play - Vidic somewhat harshly penalised for a coming together with Javier Saviola.
However, Toni saw his effort expertly saved by spot-kick specialist Handanovic and Verona's misery was compounded by a late own goal from Moras, who turned in a Danilo D’Ambrosio cross.