Scores of gunmen dressed in military uniform arrived in Bajoga, 60 kilometres from Gombe city in a convoy of 20 vehicles at about 7 am (0600 GMT).
Troops managed to push out the attackers and they then drove towards the town of Ashaka five kilometres away near the border with Yobe state to the northeast.
Both raids came after an attack on the Yobe state capital, Damaturu, on Monday, which left more than 150 people dead, including 38 police and six soldiers.
Although not as badly hit by Boko Haram violence as Yobe, Borno and Adamawa states, Gombe has seen a number of attacks, including a bus station bombing in October which killed at least eight.
Ashaka, which is home to a giant cement works owned by French group Lafarge, was hit on November 4, when fighters stole huge quantities of dynamite and several pick-up trucks from the plant.
In June, Boko Haram deployed its first female suicide bomber when a middle-aged woman detonated her explosives outside a barracks in Gombe city.
Boko Haram has frequently raided banks for funds to buy weapons, while burning down police stations, government and political party buildings is a sign of their opposition to secular rule.
In Bajoga, residents said the militants shouted "Allahu Akbar" (God is greater) and fired indiscriminately before burning down a police station in a three-hour battle with troops.
"They raided two banks and set fire to offices of political parties. They also set sections of the local government secretariat on fire," said resident Babani Ashiru.
"From where I'm standing, I can see billows of black smoke coming from different parts of the town," he added.
Troop reinforcements were sent from Gombe and a military jet which bombed the militants forced them to withdraw, said local schoolteacher Sa'adu Balarabe.
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