The hosts nearly got off to a great start when Blackman threatened early on, firing in a shot which was saved by Mikkel Andersen.
Portsmouth then went close to scoring when a superb long-range effort from Akos Buzsaky struck the woodwork and Scott Allan also had a shot blocked.
United's Neill Collins headed over and Chris Porter put a header wide.
But it was the visitors who looked the more likely scorers in the first half with Allan shooting wide after a strong run into the area and Buzsaky's drive going just over.
Harry Maguire put a shot off-target before Blackman scored from the spot in the 66th minute after Lubomir Michalik's reckless sliding tackle on Porter.