The Brazilian crossed for the Argentine forward to open the scoring in the first half before sealing the points himself in a vital victory for Walter Mazzarri's men
Rodrigo Palacio scored from close range after just 13 minutes following some good work from Jonathan, before the Brazilian doubled his side's advantage midway through the second half.
Inter's run of six games unbeaten has now seen them climb to fourth and two points clear of Fiorentina, who face Chievo on Sunday, while Verona – without a win in six home matches – lost further ground in the chase for a Europa League berth.
The late withdrawal of Yuto Nagatomo through injury saw Mazzarri hand a first Inter start to Danilo D'Ambrosio, and the visitors went agonisingly close to breaking the deadlock in the opening five minutes as Mauro Icardi headed a looping header against the bar.
Icardi then had appeals for a penalty turned down shortly afterwards as he hit the deck after going shoulder-to-shoulder with Verona defender Vangelis Moras on his way into the Verona area, but Inter did edge ahead after 13 minutes.
Jonathan carried the ball well down the right-hand side before drilling in a low cross for Palacio, who tapped home from barely three yards out to celebrate signing a new two-year contract earlier this week.
Verona had a penalty shout of their own just before the half-hour mark as Luca Toni went down theatrically under the challenge of Andrea Ranocchia, but referee Luca Banti was having none of it.
Rafael had to pull off a point-blank save when Fredy Guarin was sent through on goal by Jonathan after 33 minutes, with Verona struggling to test Samir Handanovic at the other end.
Hernanes tried his luck from distance six minutes into the second half, but sent his effort straight into the arms of a grateful Rafael before Inter had the bar rattling for a second time.
Michelangelo Albertazzi and Jonathan had a coming together on the right-hand side of the penalty area – Hernanes being denied by the woodwork after Inter were awarded the free kick.
Jonathan, who was involved in most of Inter's attacking moves, added his own name to the scoresheet in the 63rd minute, reacting well after Rafael had saved his initial effort to follow up and smash home from close range.
Moras had a glorious opportunity to reduce the deficit nine minutes later, but headed just over the crossbar from an unmarked position in the Inter box.
Hernanes almost extended the Inter lead 12 minutes from time, but his dipping effort whistled just over the target.
Handanovic was forced into a double diving save in the closing stages as Juan Iturbe and Romulo both tested the Slovenian, but Inter ultimately held on.