A quickfire start to the game from Swindon saw the Robins return from Underhill with all three points to boost their advantage at the top of the table. Ronan Murray broke clear on 14 minutes to slot home with aplomb before a second from Oliver Risser gave Town a 2-0 cushion which they never surrendered.
Town made four changes for the trip to Barnet with Raffaele De Vita, Oliver Risser and Luke Rooney coming into a much-changed midfield with Lee Holmes and Matt Ritchie missing out through injury with Simon Ferry included on the bench. The other change saw Paul Benson in for Alan Connell in the frontline.
The game started with the Robins attacking down the famous slope but play lasted just 15 seconds before Jonathan Smith was cautioned for a stern challenge on Sam Deering on the edge of the centre circle.
The visitors carved out a half-chance on 12 minutes with a surging run from right-back Joe Devera, back in familiar territory, seeing a deep cross headed narrowly over by Benson.
The 811 Town fans who had made the trip to Underhill didn't have long to wait until they had real cause to celebrate. A lofted ball over from Luke Rooney saw Murray beat the offside trap before slotting home past Dean Brill with 14 minutes on the clock.
Barnet had a great chance to level the game up with 23 minutes gone as winger Andy Yiadom ghosted through but he blazed over under pressure six yards from goal. Murray had another half-chance just before the half-hour but he shot powerfully over after collecting a throw from Devera just inside the box.
It was Swindon who got the vital second with Risser on hand to get the telling touch from close range after a deep free-kick into the box by McEveley with 32 minutes played. Rooney and McEveley were enjoying the slick surface and the Robins kept on producing quality balls into the box from both flanks with De Vita and Devera also combining well on the right. Town stopper Wes Foderingham kept his concentration and was called into action inside first half injury-time, getting down quickly to save at the feet of McLeod once again.
There were - as expected - no changes at half-time for the Robins who emerged for the second half looking to build on what had been a solid first half display. Di Canio's first change of the night came on 56 minutes with Ferry replacing Smith in the heart of the Town engine room. A promising run from Rooney on the hour saw the winger's progress halted on the edge of the box and he got up to take the free-kick, which flew narrowly over.
The second Swindon switch saw Nathan Thompson replace Rooney, which meant an unfamiliar left midfield role for the youth team graduate. Moments later De Vita was forced off with a knock and he was replaced by Alan Connell on 81 minutes.
The hosts could have got back into the game on 85 minutes with May free on the right hand edge of the box, but he delayed a shooting opportunity to allow McEveley to get back and block well. At the other end Thompson almost capped his return to action with the Town third but after a neat one-two with Murray, he flashed a shot narrowly wide. After three minutes of added time the referee called time on another good night's work from the Robins who return to Wiltshire another three points closer to a swift return to League One football.