Second-half strikes from Innes Murray and Ryan Shanley gave the Citizens some breathing space ahead of the second leg at Galabank on Friday.
The club are just a couple of months shy from moving back to their spiritual home of Meadowbank – what an added bonus it would be if they were to host the likes of Dunfermline and Falkirk next season in Scottish football's third tier.
Manager Alan Maybury made one change to the side that drew 1-1 with Dumbarton in the semi-final second leg on Saturday, Danny Jardine making way for the return of skipper Robbie McIntyre.
A carnival atmosphere greeted the sides onto the artificial surface at Ainslie Park and there was a reasonable number who had journeyed north from Dumfries and Galloway to lend their support to the club that finished third in the League Two standings.
The hosts have looked far more compact under interim boss Maybury, none more so than front pairing Ouzy See and Shanley who have formed a formidable partnership just when it matters.
City were fast out of the traps and looked in a menacing mood from the off.
Danny Handling rattled the crossbar with an effort from the edge of the 18-yard box in the ninth minute before See's header hit the woodwork for a second time in the 25th minute after goalkeeper Greg Fleming had parried a powerful Callum Crane strike from a tight angle. An almighty stramash ensued with the home players appealing for handball following some desperate Annan defending.
Handling went close again moments later as City continued to press forward at every opportunity.
Murray, on loan from City’s near neighbours Hibs, came close to seeing the net bulge with a 20-yard effort that flew just wide of the far post.
In truth, the Citizens would have been disappointed heading back to the dressing room on level pegging at the break, having gone close several times throughout an encouraging first half.
Annan produced their first shot on target a minute after the restart but goalkeeper Brian Schwake was equal to Owen Moxon's strike from 18 yards.
City deservedly went ahead moments later when Murray latched onto an incisive pass from on-loan Hearts midfielder Cammy Logan, before calmly lifting the ball over the advancing Fleming and into the net.
Murray is out of contract at Easter Road this summer and the 24-year-old won't be short of admirers after another influential display in white.
The visitors had the wind knocked out of their sails shortly after the hour mark and what a stunning piece of skill it was from former Hibs kid Shanley. The 21-year-old drew a foul from Dominic Docherty and from the resulting set-piece, curled a magnificent effort into the bottom corner from 20 yards out.
The heavens opened with just over 15 minutes remaining, with conditions becoming increasingly challenging for both sets of players in the driving rain. But City continued to press forward. Surely a third goal would put the tie to bed. Murray again went agonisingly close with a low drive, but they will be more than satisfied with a hugely satisfying night's work. Roll on Friday.