The Cobblers were quickest off the blocks and Larkin, one of five players who made their debuts in a claret shirt, delivered an excellent ninth-minute cross, which Andy Kirk headed past Phil Smith to give the home side the lead.
But Northampton's celebrations proved premature and Swindon's equaliser from the penalty spot, a minute before the break, proved particularly agonising for Larkin after his move from Chesterfield in the summer.
Swindon's star performer Christian Roberts swept a cross into the home side's penalty area and Larkin was adjudged to have handled, referee Clive Penton pointing to the spot after a quick glance to his linesman.
Roberts sent Mark Bunn the wrong way from the spot and the same player almost added to his tally three minutes after the restart, when he cut inside and unleashed a stinging left-footer which cannoned back into play off Bunn's right-hand post.
Northampton do not have a happy record at home on the opening day of the season and have now failed to win any of their last seven attempts at Sixfields.
They had plenty of chances themselves, with substitute Poul Hubertz coming closest after making his debut as a second-half substitute following his move from Millwall this week.
Hubertz saw his 78th-minute overhead kick bounce back off the top of the crossbar, but he squandered an easier opportunity when he lifted a shot over the woodwork from 12 yards in the dying minutes.
Kirk was the other culprit in front of goal. Just a minute after his opener he headed an Andy Holt cross straight at Smith and in first-half stoppage time he raced clear, only to shoot tamely with only the Swindon goalkeeper to beat.