Town fell to their first league defeat since the second game of the season as Oldland netted on the counter-attack in the 65th minute.
It put an end to Barnstaple’s 37-game unbeaten run but, with Welton Rovers and Cribbs sharing a 1-1 draw, they are uncatchable at the top of the table.
Barnstaple manager Barry Yeo’s assistant, Karl Baggaley, interrupted his dressing down of the team with the news.
“It was a bit of a weird one, I was just telling the lads what they had done wrong and giving them a talking to when Karl came in and shouted out the Welton score,” said Yeo.
“All I said was, ‘Shall us’, and we went crazy with the celebrations, I even picked up an injury.
“It was a poor game but all the hard work earlier in the season has paid off.
“I also have to pay tribute to Oldland who gave us a quality reception when they heard the news. They applauded us off the pitch and it was a great touch.”
After an away game against Almondsbury UWE on Tuesday, Barnstaple will finish the league season at home against Devizes Town next Saturday. They will then aim to complete the double against Willand Rovers in the Les Phillips Cup final at Bridport on Sunday, May 10.