Gretna came from behind to win the game after Keir Foster gave the students an early lead.
Calum Helm levelled the tie with a long range curling effort before Currie bagged a brace to ensure The Anvils’ place in the second round.
It was a great first outing for Michael McIndoe and his assistant Robbie Park, who were announced as the new permanent management team earlier this week.
Victory against Edinburgh Uni follows a run of five straight defeats for the Raydale side and this weekend they travel to face fellow Lowland League strugglers Dalbeattie Star in a must-win bottom of the table clash.
Russell Currie is back among the goals for Gretna after a recent injury, and the striker scored a brace against Edinburgh Uni following a penalty miss early on in the game.
Currie said: “A few years ago I would have went into hiding after missing a penalty, but I’m a different player now, I’ve battled through some injuries and faced new challenges every year with different teams.
“Now I’m starting to find that level of maturity, keep my head up and look for another chance.
“The Scottish Cup is a big competition, we’ve been drawn against Drumchapel United at home in the next round, we might go into the game as favourites, but anyone can win in the cup and that’s what makes it exciting.”
Ahead of this weekend’s match at Dalbeattie, he added: “The feeling has been good within the squad, we have a positive young team.
“I loved my time at Dalbeattie, but it was a lot of travelling and I bought into the project here at Gretna.
“Dalbeattie have also just had a good win in the cup and both teams will be looking forward to this weekend and hoping that they can win.”
Currie found the back of the net no less than 30 times in all competitions last season for Dalbeattie and the striker has already bagged eight so far this term.
He added: “I think I have eight goals so far this season and when I came in the gaffer was wanting me to hit 40!
“I just want to enjoy football as much as I can, the biggest thing for me is to help the team and if I can get goals along the way then that’s brilliant.”
This Saturday Dalbeattie Star v Gretna 2008, 3 pm ko at Islecroft, £8 Adults, £4 65+, Children FOC.
Gretna have also announced the signing of 29-year-old midfielder Lewis Turner from Bonnyrigg Rose for an undisclosed fee and goalkeeper Ali Adams.
Both signings will bring quality into the side as they look to push up the table.
Manager Michael McIndoe welcomed both new signings to the club, he said: “(Lewis Turner) is a great signing for the club and shows our intentions moving forward.
“He is a player with high levels of quality on the ball and a winning mentality. He will bring much needed experience to the team.
