Juvhel Tsoumou's early strike was the difference between Plymouth and Bradford in a tight battle between the League Two strugglers.
Preston loanee Tsoumou nodded Plymouth in front at the back post from Paul Wotton's free-kick.
Robbie Williams' shot hit a Bradford post before striking Bantams keeper Matt Duke and falling to safety.
Jake Cole made a double save from Guy Branston and Lee Bullock's follow-up to preserve Argyle's lead.
And Duke pulled off a stunning stop late on to keep out Wooton's piledriver.
Macclesfield's defeat at Gillingham means both sides are now four points clear of the relegation zone.
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Plymouth Argyle manager Carl Fletcher tells BBC Radio Devon:
"It could have been a lot easier for all us in the last 10 minutes than it was, but we'll take 1-0.
"Really delighted with the lads, I'm proud of them. There's so much pressure on us at the moment.
"It's going to be a really tough game next week, but we'll go into it full of confidence."