Paolo Di Canio's men dominated for long periods and were finally rewarded as Connell, the Robins' top scorer this season, fired the ball home from seven yards out in the 85th minute.
It was just rewards for the League Two table-toppers, who could have been ahead as early as the sixth minute when Paul Benson nodded a Paul Caddis cross against the crossbar.
Caddis, who was returning from a long injury lay-off, was influential throughout much of the first period and set up Simon Ferry, in 25th minute only for the midfielder's shot to be well saved by Jake Cole.
The second half was a much more even affair and Plymouth nearly grabbed the lead in 63rd minute through substitute Ashley Hemmings, who drove a shot agonisingly wide from 25 yards.
But Swindon were not to be denied as super sub Connell ensured all three points with five minutes remaining.
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