Approaching his 35th birthday, Yeo has followed Macclesfield manager Keith Alexander across the lower leagues and his talisman came up trumps with a breathtaking strike.
Having lost the first four games of the season and conceding 14 goals without mustering a reply, Macclesfield fans were delighted to see Yeo execute a pinpoint lob volley to leave keeper Dean Brill stranded in the 12th minute.
Macclesfield might have had more goals with Yeo forcing a sharp reaction save from Brill at the near post, with youngster Matthew Flynn planting a header from the resulting corner into the side-netting.
Luton showed precious little in the first half and squandered their best chance in the 33rd minute when a clearance from Flynn ricocheted off Rossi Jarvis to set up Lewis Emanuel on the edge of the box.
However, Emanuel wasted the opportunity skying it over the bar with only the keeper to beat.
Macclesfield extended their lead in the 61st minute when young defender James Jennings curled a powerful drive to the far corner with Brill unsighted.
Luton could muster little in response with Keith Keane lashing a long-range drive over the bar in the 69th minute and Tristan Plummer forcing a good low save from Jonny Brain moments later.
Macclesfield thought they had extended their lead in the 71st minute when Yeo sent a glancing header to the far corner only for it to be ruled offside.
Deep in injury time, substitute Ryan Charles mustered a late response with a pinpoint free-kick around the wall with virtually last kick of the game.