Paul Mullin fired the all important 38th minute winner but it was goalkeeper Rob Elliott who earned hero status saving a twice taken penalty from Justin Richards as well as other super saves to prevent Woking taking something from the game in which they deserved a share of the spoils.
Robbie Williams and the inspirational Gary Roberts came close for Stanley in the first half, but it was a dramatic second half that sparked the talking points as Stanley held on precariously to Mark Boyd's effort which was diverted home by Mullin.
Accrington had already survived two penalty appeals when Mullin handled Simon Jackson's cross into the box.
Richards stepped up but saw his effort saved by Elliott before the striker thumped in the rebound. Referee Simon Beck ordered a retake and incredibly Elliott's double save kept Woking out before Boyd cleared off the line from a Karl Murray header.
Amazingly Stanley spurned two sitters to seal the match when substitute Andrew Mangan failed to set up Roberts for the simplest of chances before Leam Richardson somehow hit the bar from eight yards with a goal at his mercy.
With five minutes of time added on, Stanley fans were left on tenterhooks until the final whistle but a pitch invasion signalled the end of that 44-year wait and nobody could begrudge them their triumph.
"The players deserve all the plaudits because they have won 26 games and that deserves to win any league," said Accrington's emotional boss John Coleman.
"It's a great feeling but anyone who thinks we'll clock off now couldn't be more mistaken."