Seventh-placed Roma, who have the best attacking and second-worst defensive record in the league, twice led in the first half and trailed 3-2 early in the second before Panagiotis Tachtsidis gave them a point.
Alessandro Florenzi side-footed Roma ahead in the ninth minute from Francesco Totti's pass and former AC Milan and Fiorentina striker Alberto Gilardino levelled eight minutes later as the game got off to a flying start.
Roma immediately regained the lead when Pablo Osvaldo headed in a Miralem Pjanic cross for his 11th goal of the season but again held the lead for only eight minutes before Manolo Gabbiadini hauled Bologna back with a shot on the turn.
Bologna, who won 3-2 at Roma earlier in the season, went ahead for the first time nine minutes after the break when Cristian Pasquato took advantage of a mix-up in the Roma defence.
However, Roma salvaged a point when Tachtsidis headed in a free-kick from stalwart Totti in the 74th minute.
The action continued until the final whistle with Alessandro Diaminti twice striking the woodword for Bologna.
