The 37-year-old took charge of the U's on Thursday, shortly after leaving fellow League One side Charlton Athletic.
However, the 16th-placed visitors were comprehensively defeated by Pompey, a side hoping to secure a playoff place in the table, at Fratton Park.
Oxford rattled the woodwork midway through the first half as the ball was passed to James Henry on the edge of the box and the ensuing effort was drilled onto the top of the bar.
The U's could not force an equaliser by the break, however, and when they were handed a reprieve from the penalty spot on the hour, Alex Mowatt could only strike the post.
Drama ensued as Nathan Thompson taunted the penalty taker, who responded by swinging an arm into the face of the 27-year-old, and was subsequently shown a red card.
Pompey captain Pitman made sure of all three points with his second of the game nine minutes later, a squared ball - once again from Lowe - tapped into the back of the net from close range.
PORTSMOUTH (4-1-4-1): McGee; Walkes, Whatmough, Clarke, Donohue; Thompson (May 87'); Lowe, Close, Ronan (Evans 51'), Naismith; Pitman
OXFORD UNITED (4-1-2-1-2): Eastwood; Kane, Dickie, Mousinho, Smith-Brown (Ricardinho 77'); Brannagan; Ledson, Mowatt; Henry (Mehmeti 77'); Napa (Rothwell 66'), Thomas