Midfielder Mohamed Sissoko charged superbly into the box and smashed into the top corner on 27 minutes after Palermo had struck the bar through former Juve striker Fabrizio Miccoli.
The Sicilians pushed hard for a leveller but David Trezeguet, who had been out for five months with a knee problem, sealed Juve's win with his first league goal of the campaign after good work from ex-Palermo forward Amauri.
Alessandro Del Piero was left on the bench ahead of Wednesday's Champions League clash at Chelsea.
AC Milan, in third place, host Cagliari on Sunday.
Inter forward Balotelli, out of favour with Mourinho for much of the season after the coach criticised the 18-year-old's attitude, whipped in a free kick after 82 minutes that evaded everyone in the box and nestled in the corner.
Bologna had several chances late on but Julio Cesar made two sharp saves and Inter can now focus on Tuesday's Champions League match at home to holders Manchester United.
AERIAL POWER
"At the end we suffered a lot with five or six corners in a row but we defended well," the keeper told Sky. "It is another three points before the big match. We have to stay calm."
As so often this season, champions Inter used their aerial power to score the opener from a set piece amid controversy.
Adriano, who netted with his arm in last week's 2-1 win over Milan, met Maicon's corner and again headed the ball against his shoulder before Cambiasso blasted in after 57 minutes.
Uruguayan Britos then scored his first goal for Bologna, coached by fiery former Inter assistant boss Sinisa Mihajlovic, when he headed in a corner. Cambiasso tried to block the ball on the line but got in a tangle as he avoided committing handball.
Last season's runners-up AS Roma climbed to fourth after Brazilian Rodrigo Taddei expertly curled the ball home in the 63rd minute to seal a laboured 1-0 win over visiting Siena.
Brazilian defenders Juan and Cicinho went off injured for Roma and could be doubtful for Tuesday's Champions League game at Arsenal.
