Argyle took the lead when Antoni Sarcevic swept in from the right and let fly with a rising drive that took a deflection to beat City goalkeeper Colin Doyle.
Earlier Doyle had made a fine save to deny in-form Argyle attacker Ruben Lameiras.
Bradford responded well with Paul Taylor twice forcing saves from Plymouth stopper Remi Matthews.
The first half ended with Argyle in the ascendancy, boosted by Sarcevic’s goal and a stinging Lameiras low drive that flew inches wide.
Argyle playmaker Graham Carey came close to doubling the home side’s advantage at the start of the second half but shot over after beating three players in the box.
A brilliant Bradford goal-line block by skipper Romain Vincelot denied Sarcevic as he let fly from close range after latching on to Sonny Bradley’s nod down from a Carey corner.
Bantams striker Charlie Wyke was sent off following a straight red card in the last minute of normal time after an aerial challenge with Bradley.
Rangers manager Steven Gerrard is weighing up a move for Liverpool full-back Jon Flanagan, reports claim.
Scottish champions Celtic are reportedly ready to offer full-back Calvin Miller a new deal before sending him out on loan.
Everton target Jack Wilshere has sparked a scramble for his signature after confirming he is leaving Arsenal this summer.
Tottenham's hopes of landing Wilfried Zaha have been hit by the news Crystal Palace have offered him a bumper new deal to stay.
Ryan Giggs says Gareth Bale would be the perfect fit for Manchester United but has doubts over whether he will leave Real Madrid.
Manchester City's attempts to sign Riyad Mahrez could be in doubt again as reports claim Leicester only want a straight cash deal.