The striker controlled a mis-hit Rodrigo Taddei shot and fired home in the 72nd minute as the hosts continued their remarkable recovery from the disarray they found themselves in at the start of the season.
Inter's Diego Milito had equalised just six minutes earlier with a goal that looked offside, after Roma's Daniele De Rossi opened the scoring in the 17th by capitalising on a blunder by goalkeeper Julio Cesar.
Champions Inter hit the woodwork three times, the last occasion from Milito deep in stoppage time.
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Third-placed AC Milan can pull level with Roma on 62 points with seven games to go if they overcome injuries, suspensions and poor form to beat Lazio on Sunday.
"This is a great, beautiful night," Toni told Sky television. "We've been chasing for a while.
"It was important to win tonight to try to realise a dream. Now we're a point away we'll see what happens."
CESAR ERROR
Roma were on top for most of the first half, with Mirko Vucinic and John Arne Riise going close after De Rossi tapped the ball in when Cesar spilled a Nicolas Burdisso header.
Former Roma defender Walter Samuel then roused Inter when he headed against the crossbar in the 42nd minute.
Argentine forward Milito, back after missing Wednesday's 3-0 win over Livorno with a hamstring problem, also hit the upright before scoring a goal that should probably have been disallowed for offside against Goran Pandev earlier in the move.
Toni struck soon after to extend Roma's unbeaten league run to 21 games while the post denied Milito at the death.
Roma captain Francesco Totti came off the bench in the closing stages to make his return from a long-standing knee problem.
Inter, who meet CSKA Moscow in the first leg of their Champions League quarter-final on Wednesday, may be suffering from fatigue because of their packed fixture list, having only won two of their last nine league games.
Elsewhere Palermo consolidated fourth place, which is worth a slot in next season's Champions League preliminaries, with a 3-1 home win over Bologna courtesy of a Fabrizio Miccoli hat-trick.
The striker nutmegged keeper Emiliano Viviano on 10 minutes and then restored his side's advantage with a penalty in the 43rd after Adailton had been on target from a free kick for Bologna.
Miccoli then sealed victory for the Sicilians 11 minutes from time.
Palermo have 51 points, four more than fifth-placed Sampdoria who hosted Cagliari on Sunday.
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