Boro's toothless attack never looked like breaking their goal drought with a Malcolm Christie drive from 9 yards after 65 mins, saved by Ian Bennett, their only serious effort on goal.
Birmingham continued an impressive end to their first season in the Premiership and now move above Boro in the league table after cruising to this victory.
The home side opened their account on 18 mins, Dugarry controlled a long ball in to the area and turned to volley sweetly past Mark Schwarzer. The lead was doubled on 39 mins, Clemence driving a low freekick through the Boro wall in to the net.
Lazaridis sealed the three points for Steve Bruce's men after 81 mins, converting a deep Robbie Savage cross.
Boro now cannot beat their record points tally in the Premiership after this result, their only target for the end of the season after slim hopes of European qualification were dashed. McClaren must now try to motivate his players for the final two games of the season to avoid what was once a promising season, full of potential, turning in to a disapointing exercise in treading water.
Boro's reliance on Juninho and Geremi for their creativity in attack shows them up badly when those two are missing, Riverside regulars must pray the Brazilian stays injury free next season and the Cameroon man signs a permanent deal at the club.
McClaren must ask more of his strikers, only Malcolm Christie and to some extent Szilard Nemeth emerge from this season with any credit. Massimo Maccarone, Michael Ricketts and Joseph Job must improve in front of goal to save Boro from having to dip in to the transfer market once again in search of a regular goalscorer.