Matthews, who finished second in the Atlanta 5000m but was robbed of silver by disqualification after his guide runner crossed the line ahead of him, was delighted with his performance.
Matthews, 39, a holder of the MBE, landed the 10,000m title in the T11-Blind class following an outstanding tactical performance.
He overtook race leader and favourite Carlos Ferreira of Portugal on the final lap to win in a time of 35 minutes 23.07 seconds - over three seconds ahead of his rival. Tim Willis of the United States took bronze.
Matthews, who finished second in the Atlanta 5000m but was robbed of silver by disqualification after his guide runner crossed the line ahead of him, was delighted with his performance.
"I can't believe it, it is fantastic," he said. "I have never run in an atmosphere, in a cauldron like this."
The Leamington Spa-based braille secretary, who last landed gold in Barcelona in 1992, has only recently taken up 10,000m running and is hoping this will be just one of three medals at these games.
"I go in the 5,000m and am using the marathon as a cheap way of seeing the sights," he joked. "This is my first gold for eight years and the sweetest."
Britain also took a bronze in the F56 class men's shot, with Mark Smale throwing 10.70m for third place.
Krzysztof Smorszczewski of Poland won with a new world record of 11.49m, and Denmark's Rene Nielson was second (10.74m).
Smale, 37, threw a season's best which broke the previous world record of 10.67m, but Smorszczewski smashed it with his winning effort.
In the first round of the men's tennis there was disappointment for Britain's Simon Hatt as he went down 7-5 6-4 to Colin McKeage of Canada.