The Nerazzurri struggled to break their relegation-threatened opponents down in the first half, but headed goals from Milan Skriniar and Andrea Ranocchia in the space of three minutes got them over the line.
Just a second league win in 11 matches for Inter is enough to lift them up to third place in the table, having played a game more than all the teams around them.
Benevento, who had Nicolas Viola sent off nine minutes from time for two bookable offences, outplayed their more illustrious hosts for large parts of the first half and will be aggrieved not to have registered a goal.
Sandro then wasted a good opportunity when latching on to a through-ball, with Inter - booed by their own supporters at times - failing to create much of anything.
The visitors also had a penalty appeal rejected after Ranocchia caught Danilo Cataldi inside the box, and that would be a key moment in the match as Inter were ahead on 66 minutes.
Skriniar was well positioned to dive in and head the ball over the line at the back post once it had been flicked on by Vecino.
Despite being second best for large parts, the home side had a second goal a few minutes later through Ranocchia, who converted from a similar move for his first Serie A goal in over three years.
Benevento were unable to drag themselves back into the game, and their fate was effectively sealed when losing Viola for the closing stages of a match they looked capable of winning for large parts.
INTER MILAN (4-2-3-1): Handanovic; Cancelo, Ranocchia, Skriniar, D'Ambrosio; Vecino, Gagliardini; Candreva, Rafinha (Karamoh 65'), Perisic (Brozovic 82'); Eder
BENEVENTO (4-3-3): Puggioni; Sagna, Djimsiti, Tosca, Letizia; Viola, Sandro (Del Pinto 66'), Djuricic (Cataldi 46'); Brignola, Coda (Diabate 80'), Guilherme