Wales Under-21 international Lloyd James opened the scoring after 14 minutes with his first career goal. His driven strike clipped the heels of Exeter defender Richard Duffy and flew past Paul Jones.
David Connolly then struck the crossbar for Saints, before James delivered a wonderful free-kick for Neal Trotman to head home on the half hour.
Exeter's Troy Archibald-Henville saw red ten minutes before the break for a clumsy high challenge on Morgan Schneiderlin, leaving Paul Tisdale's men with an uphill struggle.
But the Grecians battled back impressively in the second half and gave themselves a fighting chance when captain Matthew Taylor headed in Ryan Harley's corner.
As the game became stretched with Exeter pushing for an equaliser, Southampton added a third with three minutes remaining as Waigo burst clear before slotting past Jones.