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Derry were expecting the Swedes to come out all guns blazing but instead the visitors opted for a more patient approach and it was the home side which saw more of the ball early on.
Kevin McHugh, on the right side of a five-man Derry midfield had the first attempt on goal, albeit from 25 yards out in the fifth minute.
His attempt had Gothenburg goalkeeper Benjit Andersson reaching high over his head to gather the ball.
As Derry grew in confidence a McHugh ball from the right wing found O'Flynn on the left and his through-ball put Ruairdhi Higgins one-on-one with the keeper - only for his first touch to let him down six minutes later.
The Swedes' slow approach began to pay dividends as they pushed Derry further back and from a 20th-minute corner from Niclas Alexandersson they were fortunate to survive when keeper David Forde flapped and was grateful to see skipper Peter Hutton hammer it to safety.
But Gothenburg were unable to build on that spell of pressure and Derry were able to begin creating chances of their own again, not least when Hutton was only inches away with his head from Kevin Deery's right-wing cross in the 31st minute a couple of yards from goal.
And that pressure paid off when George Mourad handled a Deery corner in the 31st minute and O'Flynn kept his cool to put his spot kick just inside the upright despite the keeper going the right way to give them a two-goal lead in the tie.
Mourad was booked by Icelandic referee for the handball and possibly Derry might have had an argument for him to be sent off if it was indeed deliberate.
There was a nervy moment right at the start of the second half for City when Hutton, trying to clear an Alexandersson ball into the box headed it back towards his own goal but Darren Kelly was able to clear.
Derry almost had a second on the night when McHugh got around Hjalmar Johnsson on the right and deliver a perfect cross to the back post, where Higgins just failed to get enough on his header to guide it home.
It was a measure of how desperate the Swedes were becoming that Magnus Kihlberg decided to half-volley the ball towards Forde's goal from all of 35 yards in the 67th minute, the ball flying high over the bar. At that stage the City keeper had still not had a serious save to make.
There was high drama when the referee awarded a penalty when substitute Marcus Berg went down under a Forde challenge in the 75th minute.
But the linesman had already indicated a goal-kick and after a consultation he changed his mind and booked the Swede for diving.