Former Bantam Gareth Evans gave a dominant Pompey the lead with a brilliantly struck 22nd-minute penalty following a foul on Oli Hawkins.
Tom Naylor doubled the lead from close range three minutes before half-time.
Play was momentarily stopped when a drone was spotted by the referee hovering above Fratton Park and the players were ordered to the side of the pitch.
Hope Akpan got Bradford - whose manager David Hopkin quit earlier this week - back in the game in the 65th minute, stabbing home after a goalmouth scramble.
The comeback was short lived as Jamal Lowe bundled in Lee Brown’s cross to make it 3-1 two minutes later.
Close made it four by stretching to divert Evans’ wayward half-volley beyond the diving Richard O’Donnell and he put the gloss on the win by grabbing his second late on from Ronan Curtis’ centre.
Pompey are fourth, five points off the automatic promotion places, while the Bantams remain 23rd, six points from safety.