Early goals from strikers Samuel Eto'o and Diego Milito put the champions in control but Cesena stunned the Inter faithful when Erjon Bogdani and Emanuele Giaccherini levelled the scores, only for Cristian Chivu to restore Inter's lead before half-time.
Inter moved ahead of Juventus and Roma with their fourth successive league win since coach Leonardo took over from Rafa Benitez.
"We started excellently, but all credit to Cesena," the Brazilian coach told reporters. "Psychologically we weren't prepared for their comeback. Our defence had had nothing to do until then and we were ragged.
"But I'm pleased with how they recovered in the second half and in the end we deserved the win."
The Nerazzurri and Eto'o in particular began as they had left off after their 4-1 demolition of Bologna at the weekend.
With 14 minutes on the clock, the Cameroonian played a typical give-and-go with Milito before dribbling into the area and firing an unstoppable cross-shot low into the corner for his 12th goal of the season.
A minute later the home side were two goals to the good as Eto'o slipped in Goran Pandev who unselfishly squared for Milito to side-foot into an empty net.
It was devastating stuff from the rejuvenated European and Italian champions, but after Milito limped off on 20 minutes the Serie A newcomers struck back.
Bogdani chested down a long pass close to the penalty spot, turned and fired into the corner in one movement and six minutes later, Giaccherini ghosted into the box and volleyed home Luis Jimenez's clipped pass.
But just as it looked as though the sides would go into the dressing-rooms level, Chivu spared Leonardo a stiff half-time team talk when he rose highest to head home Maicon's perfect right-wing centre.
In a much more subdued second period, Eto'o smashed the ball against the crossbar on 66 minutes before Cesena were reduced to 10 men when Giaccherini was sent off for a second caution.
Pandev should have saved the home fans late worries but blazed a good chance over and Igor Budan twice went close for Cesena in the dying minutes to suggest Leonardo still has work to do if Inter are to win a sixth successive scudetto.
