East Fife were unable to build on their win at Hampden and make it two away wins on the bounce.
Despite having large spells of possession, they couldn’t make it count and goals from Josh Watt and Rabin Omar separated the sides.
It was the home side who started by far the better of the two and Ryan Goodfellow had to be at his best to keep out Todd and Peter Weatherston efforts.
At the other end Kevin Smith will feel he should have done better with a strike he pulled wide from just a few yards out.
The Fifers settled well after a dodgy start to the game and went on to dominate.
Jonathan Page was afforded a sight of goal from eight yards but he got under his shot and cleared the bar.
Annan took the lead shortly before the break with a poor goal from East Fife’s point of view.
From a corner Kyle Wilkie lost possession on the edge of the Annan box.
The home side broke away through Smart Osadolor who ran the length of the park before playing in Todd who netted.
Annan were unlucky not to go further ahead in the second half when Weatherston burst in on goal and crashed an effort off the bar.
The Fifers pushed Jonathan Page up front in the hunt for an equaliser but Annan exploited the gap he left at the back.
Omar burst in on the East Fife goal and wrapped up the win with a second.
East Fife boss Gary Naysmith said: “Annan had more goal scoring opportunities than us so for that fact probably deserved to win.
“They worked very hard on a surface that they’re used to.
“I’m not looking for excuses but it’s not for me that surface.
“I don’t mean artificial surfaces in general, I just mean that one.
“The amount of players slipping wasn’t right.
“But it’s not an excuse because Annan worked hard and have a system that works for them.
“They have a very, very good home record and you have to be at your very best to get something and we weren’t.”