Inter — which had lost at home to Udinese and CSKA Moscow over the past week — moved level with Cagliari, Roma and Catania in eighth, 12 points back, by defeating Fiorentina at the San Siro.
Claudio Pazzini used one sublime touch from a sharp angle to redirect a long pass from Coutinho past Fiorentina goalkeeper Artur Boruc in the 41st.
Last week, Pazzini slipped and fired a penalty over the bar in the loss to Udinese, but he can put that painful memory behind him now.
Nagatomo's goal involved a bit of good fortune, as he ran into a failed clearing attempt by defender Manuel Pasqual and the ball bounced in off his chest. It was Nagatomo's third goal since joining Inter in January.
Inter manager Claudio Ranieri refused to speculate if this victory might mark a turnaround for his squad.
"Let's not talk about a turnaround. We've already used that word too many times lately," he said. "But it was a great performance, and the fans were magnificent. They encouraged the squad from the opening minutes."
Inter was helped by the return of right back Maicon after more than a month out with a left thigh muscle injury.
"He's run up that wing thousands of times and he knows what he's doing," Ranieri said.
In Siena, Rossi scored from the centre of the area in the 56th after goalkeeper Zeljko Brkic was left out of position having failed to intercept a cross, and Palacio scored into an empty net after dribbling by Brkic in stoppage time.
The win moved Genoa into seventh place, 11 points back.
In Palermo, Cesena had already hit the crossbar before Mutu connected on a long header off a corner in the 63rd.
A minute later, Palermo was reduced to 10 men when Ezequiel Munoz picked up his second yellow card.
Cesena moved within two points of escaping the relegation zone.
