Lee Cook's fourth-minute shot from the right-hand side of the penalty box was enough to separate the sides.
Brendan Moore denied Cook a second in the first half while Angus MacDonald twice went close for the Gulls.
Torquay, who had been on an eight-game unbeaten run, have now lost two in a row and are two points from safety.
They have scored just one goal in their last six games and dropped to third from bottom of the table after Boreham Wood's 3-0 win over Dover.
Eastleigh moved to within two points of the National League play-off places as they won at relegation-threatened Torquay United.