A first-half header from Paul Robinson was enough for Blues to pick up their fourth successive win and climb into second spot in the Championship.
The visitors started the game positively and Jacques Maghoma was in-behind the Bolton defence within the first minute but his cross failed to find Andy Shinnie.
After threatening on a couple of occasions without managing to test Ben Amos, Blues took the lead after 20 minutes. Robinson's second goal in as many games broke the deadlock after the defender met an excellent free-kick from Demarai Gray at the far post.
Blues could have doubled their lead 10 minutes later when another dangerous delivery from Gray fell to Michael Morrison but he was denied by three last-ditch blocks from the Bolton rearguard.
As the opening 45 minutes drew to a close the hosts rallied and saw a couple of chances go begging. Tomasz Kuszczak beat away an effort from Liam Feeney before Emile Heskey failed to get telling contact on a Jose Manuel Casado free-kick.
The home fans thought Wellington had won a penalty after 41 minutes but referee Geoff Eltringham penalised the winger for simulation.
After the interval both sides pushed for the next goal with Blues first to go close. Gray broke powerfully through the middle and fed Shinnie but after twisting and turning his way into the box, Amos stood tall to deny him.
Next it was Bolton's turn and but for some heroic Blues defending would have been level. Feeney found acres of space inside the penalty area and drew a fine save from Kuszczak, Madine pounced on the rebound but only found the frame of Morrison on the line. That clearance then fell to Darren Pratley on the penalty spot, Morrison again the man to deny him. Blues were certainly being made to work hard for a clean sheet.
Five minutes later Shinnie should have put the game to bed. Gray again the provider with a strong run and pass but the midfielder could not slip the finish under Amos.
The hosts threw everything at Blues to try and force an equaliser but Morrison and co. stood firm to secure another valuable, and hard-earned, three points.