Burnett (13-3) dominated Chicago on no hits until Adrian Cardenas -- called up from the minor leagues before the game -- lined a pinch-hit single to right field with one out in the eighth.
The right-hander went on to win his third straight start, issuing a pair of walks and striking out eight en route the victory, which snapped a two-game Pirates skid.
Neil Walker put the Pirates ahead with a first-inning grand slam and later added a sacrifice fly to drive in all five Pittsburgh runs.
Cubs starter Casey Coleman (0-2) was tagged for four runs on seven hits over 4 2/3 innings.
Celebrity Families of 2014 [PHOTOS]