Campbell acquitted himself well in the opening round, landing the cleaner shots in the early exchanges.
However, the Bulgarian edged himself in front by one point, courtesy of his superior work rate.
The fighters were very evenly matched and, after an even second, the stage was set for a grandstand finish.
Both men took turns to attack each other in the third, but most of the shots were caught on the gloves.
Campbell struck with a decent straight left and, as the Bulgarian started to look tired, it was Campbell who was finishing strongly.
The Brit landed with more combinations that seemed to batter the guard of Dalakliev, who was in survival mode by now.
in the end, the judges rewarded Campbell for his effort with a narrow 16-15 verdict.