The world champions, who put on a much improved display compared to recent matches, are now four points clear of second-placed Ireland and with two to play and need just a draw against the Irish in Dublin on October 10 to progress.
Left back Grosso, drafted back into the side after Saturday's uninspiring 2-0 win in Georgia, opened the scoring after 11 minutes when he volleyed in off the bar following Andrea Pirlo's delightful dink into the box.
"In the first half it was a spectacle and it was entertainment," he told Rai television.
"There was a lot of technical quality and two splendid goals. We are not at the top of our game, some other teams are ahead of us but we have controlled the match."
MORE URGENCY
His side generally had much more urgency and Juve's Claudio Marchisio did a good job in the problem left midfield spot having seen the birth of his child and recovered from a thigh knock in time to make his second cap.
Italy's most attacking display of the last few months meant the Azzurri left gaps at the back but Bulgaria lacked conviction when it mattered despite having several chances.
The visitors thought the ball had crossed the line when Gianluigi Buffon clawed out Stilian Petrov's first-half effort following a corner but replays were inconclusive.
