Substitute Alan Connell's late winner left Swindon on the brink of promotion to League One as they saw off Plymouth at the County Ground.
Connell sealed victory with a shot on the turn from seven yards.
The Robins will have to wait until Tuesday's League Two trip to Aldershot for their next chance to secure a top-three place.
Promotion rivals Torquay United and Crawley Town both drew meaning Swindon need a point to go up.
Paul Benson went close to opening the scoring for Swindon in the first half when he nodded a Paul Caddis cross against the crossbar.
Ashley Hemmings almost put Plymouth ahead after the break but his shot went agonisingly wide.
VIEWS FROM THE DRESSING ROOM
Plymouth Argyle manager Carl Fletcher told BBC Radio Devon:
"We were disappointed after the goal came in late. We felt we didn't deserve to lose.
"We knew they would come out strong. We did our job in the first half, but we were a bit better in the second half with the players getting stronger and stronger.
"Everybody worked hard defensively. The lads are disappointed."
Swindon Town 35 Foderingham 02 McEveley Booked 04 Flint Booked 05 Devera 07 Caddis 08 Ferry 13 Risser (Smith - 74' ) 22 Holmes 09 Benson 23 De Vita (Rooney - 58' ) 34 Murray (Connell - 55' Booked ) Substitutes 15 Thompson 19 Rooney 21 Gabilondo 24 Smith 17 Connell Plymouth Argyle 23 Cole 02 Berry 05 Purse 14 Bhasera Booked 22 Blanchard 03 Williams 08 Walton (Hourihane - 87' ) 15 Young 19 Wotton 11 Feeney Booked (Fletcher - 73' ) 32 MacDonald (Hemmings - 62' ) Substitutes 01 Larrieu 07 Daley 20 Hourihane 10 Fletcher 31 Hemmings