Kris Boyd's first-half header was cancelled out by a Tomas Danilevicius spot-kick after Mikoliunas, on as an interval substitute, threw himself down in the penalty area following a Fletcher challenge.
Scotland goalkeeper Craig Gordon remonstrated with his former Tynecastle team-mate while Fletcher later accused the Lithuanian of cheating.
The spot-kick which drew the visitors level might have seen Mikoliunas sever his ties with Hearts and leave Scotland, had goals from Stephen McManus and substitute James McFadden not given the home side all three points.
Manchester United midfielder Fletcher said: "There is no place for that football, it's a fellow professional you are cheating. It's hard to take when something like that goes against you because it was such an important game.
"I couldn't believe it was given when I didn't touch him. To give away a penalty like that leaves a sick feeling in your stomach but you have to get it out of your mind.
"It would have been devastating to have dropped points because of a decision like that but I'm glad we got the goals to get the victory.
"The last word is ours, we've won the match and that's what it comes down to."
Fletcher refused Mikoliunas' offer to swap shirts at the end of the match and Scotland boss Alex McLeish shrugged: "That's Darren's choice, that's his call. I don't have any problems with that at all.
"Mikoliunas has won his team a penalty and they would have been happy going back on the plane with a point and it wouldn't have mattered that there was simulation."