Having lost their position in the top four for the first time since the beginning weeks of the season last weekend following their derby defeat by Roma, Lazio quickly set themselves back on track.
Udinese can reclaim fourth place, though, if they beat Catania at home on Sunday.
"We proved we've got character because it wasn't easy to pick ourselves up after the derby defeat," said Lazio captain Stefano Mauri.
Zarate gave Lazio a dream start on two minutes as he turned home a cross from Mauri.
The rest of the half was a tepid affair until Cesena goalkeeper Francesco Antonioli made a fine save from a Giuseppe Biava header just before the break.
Antonioli was again called into action at the start of the second period, brilliantly tipping a Giuseppe Sculli header onto the post to keep the visitors in the game.
Zarate almost put the game beyond Cesena nine minutes from time but shot just wide of the upright.
However, there was an ugly incident as Brazilian midfielder Matuzalem was caught on television cameras punching Luis Jimenez in the face.
The referee did not see it but the Lazio player could face a hefty ban.
Lazio were also guilty of petulant and violent behaviour during the derby, in which they had two players sent off.
Coach Edy Reja admitted this had to change.
"On the pitch I didn't realise that Matuzalem punched Jimenez. Obviously there was beforehand some verbal offence but it's still an action that must be condemned," he said.
"We carried some tension with us because we also saw (a punch by the banned Stefan) Radu at the end of the derby.
"These are things that have no place in football. Sometimes you lose your heads but it's not easy to remain balanced in Rome, especially with the accumulation of tension after losing the derby."
Leaders AC Milan travel to Palermo in the day's late game, looking to extend the gap to their chasers as the Sicilians aim to end a run of five straight defeats.
Lazio back in Champions League reckoning
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