Borriello opened the scoring in the 57th minute after linking up well with Ciro Immobile before the much-travelled striker sealed the points with a fine finish in the 73rd minute.
The victory lifts Genoa out of the relegation zone and they are now just one spot and one point below 16th-placed Bologna, whose miserable afternoon was made complete when they saw midfielder Tiberio Guarente sent off in stoppage time.
Genoa entered the match looking to build on back-to-back draws against Torino and Inter Milan in their final two matches of 2012, and they came closest to a goal in a low-key first half when Immobile saw his 33rd-minute cross-shot tipped over by Federico Agliardi.
The first decent opening of the second period saw Genoa take the lead.
A great one-two between Borriello and Immobile put the Italy cap through on goal and, with only Agliardi to beat, he found the bottom-right corner of the net.
Borriello doubled his account for the night 16 minutes later when the former AC Milan, Juventus and Roma hitman drilled home a right-footed shot from the edge of the box which left Agliardi with no chance to save.
Agliardi did manage to prevent Genoa substitute Felipe Seymour from making it 3-0 in the closing stages, but it was scant consolation for Bologna, who finished the match with 10 men when Guarente was booked twice inside a minute, the first for a poor challenge and the second for complaining to the referee.