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  Winger Niall McGinn also netted as Northern Ireland recovered from their opening defeat by Poland to remain in contention for a place in the last 16.
  "People had written us off, nobody gave us a chance," said defender McAuley. "It's a very special moment.
  "We weren't at it against Poland and we wanted to put it right."
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  The 36-year-old West Brom player became the second-oldest goalscorer at a European Championship by putting Northern Ireland ahead with a 49th-minute header, before substitute McGinn added the second in injury time.
  It was Northern Ireland's first victory at a major tournament finals in 34 years - since beating hosts Spain at the 1982 World Cup - and the result means Michael O'Neill's side can still progress as a best third-placed team at least.
  They face Germany in their final Group C game and, with Ukraine having been eliminated, Northern Ireland will qualify for the knockout stages with a win in Paris on Tuesday.
  "We let ourselves down against Poland in terms of the intensity we wanted to play at so we had a point to prove to ourselves," said McAuley.
  "It was a wonderful team performance and we are delighted for everyone, especially the supporters.
  "We have something to play for in our last game against Germany, which is what we wanted. We can take a lot of confidence into that game."
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  O'Neill made five changes for his side's second group game, including leaving striker Kyle Lafferty on the bench, and the Northern Ireland boss acknowledge it was a gamble.
  "There was some risk attached to changing the team but it was a fantastic performance from the entire side," said the 46-year-old.
  "I couldn't have asked any more. The players gave every last ounce of passion and energy and the supporters were magnificent - everything that is good about Northern Ireland was in that stadium.
  "We have given ourselves a great chance of finishing third and we will try to nick a point, maybe more, against the Germans.
  "I'll let the players enjoy this and then our minds will switch to Germany. We won't underestimate them."
target: Northern Ireland goalscorer Gareth McAuley says Thursday's 2-0 Euro 2016 win over Ukraine - their first at a European Championship - was "massive".