Howe, who left Bournemouth to take over the Clarets last week, saw goals from Jay Rodriguez and Dean Marney secure only their second away win of the season. John Utaka cancelled out Rodriguez's opener for Pompey but a superb overhead kick from Marney sealed the victory.
"I'm delighted with the players. I thought they were magnificent," said Howe.
"In the first half we controlled the game and were excellent, and in the second half we really dug in and protected the lead when we needed to.
"The lads showed fantastic commitment and desire - all the hallmarks of a performance you need away from home. Our attitude was spot on.
"You can't fault any of the lads. I thought they ran themselves into the ground. They need a couple of easy days now because they really did put a good shift in."