The Bantams came into the game after losing consecutive away matches at Cambridge United and Newport County but never looked like being second best in this fixture after Ben Richards-Everton's header gave them the lead after six minutes.
Plymouth ended the game with nine men after captain Gary Sawyer was shown a red card for a high challenge on Dylan Connolly in the first half before the Irishman was then fouled in the latter stages of the contest by Antoni Sarcevic who was given a second yellow.
Connolly's first goal in English football was the highlight of the afternoon as he took one touch to get a clearance out of his feet and place his shot right into the top corner from 25 yards in first-half stoppage time.
Nine-man Argyle gave Bradford some cause for concern, however, as Ryan Hardie squeezed the ball through Richard O'Donnell's legs to reduce the deficit in the 87th minute.
But the Bantams survived the nervy ending to make it two wins from five games since Stuart McCall's return to Valley Parade.
Bradford have now picked up 38 points on home soil this season, a total only bettered by second-placed Crewe Alexandra.
Plymouth made the long trip to West Yorkshire with one of the best away records in League Two, with only two sides boasting a better points tally on the road prior to kick off.
Bradford have claimed seven points from a possible nine on home soil since McCall's reappointment, with this latest victory giving City something to build from.
In the first half, Lee Novak nearly doubled the lead after Richard-Everton's opener but his low driven shot was superbly blocked by Sawyer.
The first big opportunity for Argyle came just before the 15-minute mark when a cross went across the box towards Callum McFadzean but he snatched at his effort as O'Donnell rushed out to smother the effort.
Connolly was getting down the flanks with purpose and played a great ball across the face of goal just after the half-hour mark but no City player was there to tuck it into the open net.
Then came the first Plymouth red card as Sawyer lunged recklessly towards Connolly, leaving referee Carl Boyeson with little choice but to send the Plymouth captain for an early shower.
On the stroke of half time the lead was doubled when Connolly curled a beautiful strike into the top corner from 25 yards.
The hectic end to the first 45 minutes continued into the second half as both sides had chances to add to the scoreline.
Novak and Connolly had shots smartly saved by Alex Palmer while Clayton Donaldson missed a sitter from five yards out.
Plymouth could have been back in it at the other end but Niall Cavanan blazed over from the edge of the six-yard box.
Antoni Sarcevic, who was Plymouth's biggest goal threat with 10 goals and six assists this term, was sent off for a second yellow card after a challenge on Connolly. His first yellow came for talking back to the referee.
Hardie halved the deficit as he squeezed the ball through O'Donnell's legs at the near post but the hosts held on for a vaulable three points.
Bradford City: O'Donnell; Mellor (Henley 74), O'Connor, Richards-Everton, Wood; Connolly, Reeves, Akpan (Cooke 83), McCartan (Mottley-Henry 77); Novak, Donaldson. Unused substitutes: McGee, Pritchard, Ismail, Cooke, Devitt.
Plymouth Argyle: Palmer; Edwards (Hardie 45), Wootton, Canavan, Sawyer, McFadzean; Mayor, Bakinson (Telford 80), Sarcevic, Jephcott (Taylor 45), Moore. Unused substitutes: Cooper, Grant, Randell, Cooper.
Referee: Carl Boyeson (East Yorkshire).