The Rossoblu remain winless under new coach Davide Ballardini, who replaced Stefano Pioli earlier this month, but the point earned in Genoa puts a chink of daylight between them and 18th-placed Sassuolo.
Samp were poised to climb above 12th-placed Atalanta having taken the lead through Manolo Gabbiadini after an hour's play, but Sinisa Mihajlovic was ultimately unable to deliver the fourth Serie A win of his tenure.
Samp threatened first as Eder weaved down the left wing to unleash a shot to the near post, Gianluca Curci watching the ball sail wide, and in the seventh minute the Bologna keeper made a low save from Gabbiadini's cross-cum-shot.
Bologna took a while to get going but came close to opening the scoring in the 20th minute. Diamanti and Gyorgy Garics combined to tee up Rolando Bianchi but the striker swung and missed the ball by a few inches.
The visitors were denied the encouragement of their coach from the half-hour mark onwards as Ballardini was sent to the stands for unleashing a volley of abuse from the dugout.
Back on the pitch, Gabbiadini's long-range effort took an unfortunate deflection off Mikael Antonsson and Daniele Gastaldello managed to clear Diamanti's drive to the far post.
The scoreline would remain level at the interval as Curci took the ball off Robert Soriano's feet just before the Samp striker could let rip.
Samp claimed a deserved opening goal shortly after the hour mark as Eder's daisy-cutter found Gabbiadini in a good position to tap home.
Bologna responded brightly as Lazaros Christodoulopoulos took aim at the end of a swift counter-attack, but the Greek winger could not find the target.
Defender Gastaldello reached a shooting position in the 70th minute, only to see his effort deflected wide, and Samp responded through Eder, the Brazilian shaving paint off a post from the right-hand side of the area.
The few bright shoots of promise from Bologna finally produced into a goal as Diamanti forced the draw on the stroke of full-time.
The former West Ham forward, who has been linked with a move to Asian Champions League winners Guangzhou Evergrande of China during the transfer window, picked his spot from 11 metres and Andrea Da Costa could do nothing.