The hosts took the lead at the Amex Elite Football Performance Centre after 24 minutes when Baldock finished high into the net.
Boro continued to apply pressure and it was 1-1 on 60 minutes after Lewis Wing took advantage of the windy conditions to score direct from a corner.
Brighton were back in front just 10 minutes later as George Cox scored from the penaly spot after Jiri Skalak was brought down.
It was 2-2 in stoppage time thanks to another penalty, this time George Miller scoring his ninth goal of the season to rescue a point.
Brighton's next PL2 match is away to Southampton on Monday 30 October while Middlesbrough host Wolves the day before.