The hosts forged the game's first goalscoring opportunity, with Manchester United's Lingard firing narrowly wide following a knock-down from teammate Nikola Zigic.
It would not be long before the 20-year-old found himself with another opportunity to open the scoring, though, as Lingard capitalised on a defensive error from Gary MacKenzie and slipped his effort beyond Matt Gilks to give the Blues a 1-0 lead.
The advantage would prove short-lived, as Thomas Ince's teasing cross found Fuller, who produced a smart finish from six yards to restore parity.
Goalkeeper Darren Randolph had to be alert to deny Fuller a quick-fire brace on the stroke of half time, as the Republic of Ireland international produced a good save to deny the Jamaican.
Blues manager Lee Clark handed duo Dariusz Dudka and Aaron McLean their Birmingham debuts midway through the second half - the former of whom came close to marking the occasion in superb fashion, volleying narrowly from outside the area.
Clark's men forced the issue in the dying stages, only to be denied by the intervention of Tyler Blackett, who produced two goal-line clearances to save the Tangerines.
Debutant McLean spurned the opportunity to steal the points in the closing moments, firing straight into the chest of Gilks as both managers were forced to settle for a share of the spoils.