It was a bright start from hosting Crawley, who broke the deadlock in just the second minute. Gavin Tomlin played in Izale McLeod and, with visiting goalkeeper Ben Alnwick committed, the striker slotted his shot into the far corner of the net.
Peterborough's response to falling behind was positive, though, with both Conor Washington and Burgess failing to make connections with crosses into the area.
Both sides went on to create a number of chances throughout the remainder of the half, with the best arguably falling for Crawley defender Dean Leacock, but his volley was saved by Alnwick.
Yet, just when it appeared that the two teams were going to head into the break level, Burgess found himself with enough space inside the Crawley area to convert Jon Taylor's cross in the 40th minute.