Mark Cooper's Robins had lost their last two fixtures but a Luongo brace and goals from N'Guessan, Nile Ranger and Nathan Byrne ensured the lull was shortlived.
N'Guessan netted his sixth of the season after 24 minutes to open the scoring, rising unmarked to meet a Jay McEveley cross in blustery conditions.
The former Leicester man then beat a defender before laying the ball on a plate for Ranger to tap in his fifth of the campaign after 50 minutes.
Both sides started the day on 20 points but the game was over before the hour mark when Luongo cut inside and curled a shot past goalkeeper Chris Neal.
Vale did not make it comfortable for the home side though and top scorer Tom Pope rounded Wes Foderingham to pull a goal back after 73 minutes.
The County Ground was silenced with 10 minutes left when Lee Hughes smashed home from two yards out when Swindon failed to clear a cross.
Two minutes later though and the nerves were settled when Byrne scored the best goal of the afternoon, curling in from the edge of the box, before Luongo put the icing on the cake in the final moments - crashing a shot in after some silky skills.