Chris Johnston and Ayrton Sonkur scored in the first half, however Stenhousemuir rallied with a powerful display in the second 45 minutes that was unlucky not to be rewarded with a goal.
Annan took the lead on eight minutes when Aidan Smith teed up Johnston who drilled low into the net and a second goal arrived six minutes from the break when Sonkur headed in a Johnston corner despite Stenhousemuir claims that the ball had not crossed the line.
The visitors were on top after the break. David Marsh’s close-range shot was blocked by Alex Mitchell just after the hour and Andy Munro turned a good opportunity wide with seven minutes left.
In the other semi-final Clyde won 1-0 at Ainslie Park against an Edinburgh City side that hit the bar three times.
The Citizens’ Conrad Balatoni headed against the woodwork before Clyde took the lead on 15 minutes when Kristoffer Syvertsen netted a David Goodwillie cut back.
City were determined to get level and Josh Walker was denied early after the restart when his 20-yard shot was blocked, with Scott Shepherd hitting the frame of the goal twice in the last 14 minutes.