Patrick Agyemang also went close for the hosts while Chris Dickson wasted two chances for the Daggers.
The victory was Pompey's first since beating Exeter 3-2 on 2 November.
VIEW FROM THE DRESSING ROOM
Portsmouth manager Richie Barker told BBC Radio Solent:
"Obviously very pleased, relieved, quite proud of the players to be fair. I was, I thought, justified in my criticism last week; you have to take the good bits with the bad bits and I have to say I can't give them enough praise today. Maybe they needed a kick up the backside, I don't know, but their response today was fantastic.
"I thought in the first half the football was excellent. In the second half I thought they showed a real desire to not lose the game so if we can put the two together, then who knows, but there's a long way to go yet.
"I'm pleased for the supporters that they've got something to sing about and enjoy their Christmas."
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