Mahmood produced an excellent spell, picking five for 24 with his medium pace to restrict Hampshire to 121 for eight in 20 overs after the English side was asked to bat.
Mahmood also scored a fine unbeaten 55 off 31 balls as Aces made 123 for two with 33 balls to spare. The former Pakistan international, now a British citizen, was adjudged as Man of the Match.
Put in, Hampshire, riding on a fine run-a-ball 65 by opening batsman Michael Carberry, scored a below par 121. Carberry was the last man to fall and he didn't get any support from the other end.
In reply, Aces were off to a good start with Martin Guptill, 38 off 31 balls, and Luo Vincent (19) adding 49 runs inside six overs for the first-wicket stand.
Mahmood stole the limelight with his brilliant 31-ball knock that was studded with four sixes and five fours to take the team home safely.