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While the team effort was far from convincing, the Nerazzurri's in-form Argentina forward struck early to secure the narrow victory that moves them level on points with third-placed Juventus in Serie A.
Martinez has now netted three times in four appearances since his national team's FIFA World Cup success, while he took his league tally for the campaign to nine goals.
Meanwhile, Inter maintained its record of having never lost a top-flight match against Verona on home soil, where it has won each of its past eight games.
Inter broke through after just three minutes when the ball fell kindly for Martinez following Henrikh Mkhitaryan's promising burst into the Verona penalty area, and the striker neatly guided it into the far corner.
No side has scored more first-half goals than Inter in Serie A this season, and it looked to build on that strong start, Martinez heading straight at Lorenzo Montipo from Roberto Gagliardini's cross.
Referee Michael Fabbri waved away a penalty appeal from the hosts just before the break, despite Fabio Depaoli appearing to deflect Mkhitaryan's shot behind with his arm.
Inter thought it had doubled the advantage in the 63rd minute when Martinez brilliantly dinked the ball over the advancing Montipo, only to be denied for an earlier foul on Pawel Dawidowicz.
Winless in their previous 22 clashes with Inter since a 1-0 victory in February 1992, Verona went close to an equaliser when Sulemana's low drive from a tight angle called Andre Onana into action with 20 minutes remaining.
Substitute Kristjan Asllani almost put a seal on victory with a spectacular long-range effort, but Martinez's early strike proved enough for the hosts.