Kevin Webster struck the first of a match-winning double from a direct free-kick after 48 minutes.
Buckie's Ian Murray is still seeking his 200th Highland League career goal after Saturday's draw but is more concerned with clinching the title.
Kevin Small's early red card for Thistle made it a tough battle but Murray said: "It wasn't about me today. It was all about taking us closer to a first Highland League title in over 50 years. I think if anyone doubted us, today proved the kind of spirit we have."
Deveronvale's challenge fizzled out after a 2-1 defeat at Turriff, but the biggest surprise of the day came at Huntly where fast-improving Fort William enjoyed a shock 3-1 win.
Formartine beat Inverurie Locos 3-1, while Forres thrashed Strathspey Thistle 5-1.
In the Fosters Highland League Cup quarter-finals, goals from Jamie Lennox and Cammy Keith sent Keith through 2-0 against Nairn. Administration-hit Clach crashed out 3-0 at Rothes with Ian Macrae, Stuart Fettes and Kris Duncan on the mark.