Zola was appointed as the successor to the sacked Gary Rowett with the club in seventh place, three points off third in the Championship, and leaves them in 20th and three points off the relegation zone.
The visitors completed the season double over Birmingham thanks to goals in either half from Lloyd Dyer and Lucas Akins.
Burton's second goal prompted an immediate chant of "we want Zola out" from the disgruntled home fans, and they got their wish soon after full-time with the Italian handing in his notice.
Birmingham had picked up just four points from a possible 27 under the Italian and Monday's display was another poor, disjointed and dejected performance from a demoralised Blues side who slipped ever closer to relegation.
The result leaves them worryingly close to the bottom three and with only three matches for Zola's replacement to turn things round - starting with Sunday's trip to Aston Villa.