Ricky-Jade Jones scored a stoppage-time penalty to break Crawley hearts after the Reds had twice fought back to level after a first half hat-trick from Abraham Odoh.
Posh are now nine points clear of Burton Albion with seven games to go and all but safe from any relegation threat.
They will be confident of picking up three more points at the weekend with relegation-threatened Northampton Town coming to town.
Here is where a supercomputer – produced by footballwebpages.co.uk – believes Posh will now finish the season.
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