This will be the Republic’s eighth play-off appearance for either a World Cup or European Championship - making them the most experienced nation in such situations.
Ireland saw off Bosnia and Herzegovina in a play-off for Euro 2016 and, after being drawn against Denmark this time out, O’Neill wants to tap into the memories of those games.
“I think we can draw from that experience,” he insisted last night. “We had two games against Bosnia, two very difficult games for us. The (away) game was shrouded in fog in the second half and we got that elusive away goal and were able to carry that momentum into Dublin. Because it is not that long ago I think we can draw something from that.
“Two games in quick succession, the turnover being very quick. Lets just go for it. We are delighted to be here first of all, we had a great win against Wales to propel us here and now let’s take our chance.
“I’m delighted to be drawn away from home first so we will try and get some sort of advantage, or certainly negate Denmark’s advantage before we get to Dublin. It would a terrific achievement if we could make it.”
Denark are regarded as the 19th best nation in the world were the lowest-ranked of the seeded teams for Tuesday’s draw in Zurich.
Republic of Ireland manager Martin O’Neill believes his players will hold no fear of trying to secure a positive result in Denmark, but they will be wary of “players at the top of their form for big clubs”.
Speaking to RTÉ, O’Neill said: “The second match is in Dublin and I hope that we still have something to play for by the time that we get there.
“All of those teams that were unseeded probably didn’t want to play Italy so there was a 50/50 chance of getting them from that viewpoint.
“It’s going to be a difficult game for us. We’ll take our chance. You just have to leave it to fate. The draw is the draw regardless, come what may.
“Our away record in this particular competition has been very, very strong which is great news. I don’t think the players will fear that, but I think they will be very wary. They have players that are playing not only at the top of their form but playing for big clubs as well too.”
Ireland are only seven places beneath them in the latest FIFA rankings and goalkeeper Darren Randolph admits Denmark was the tie he was hoping to land.
“I think everyone will be very happy with that draw, being away first leg and obviously second leg way in Dublin,” he said.
“That was probably who I was looking out for yes, I’m happy with that draw.”
Meanwhile, Randolph’s Middlesbrough team-mate Cyrus Christie wants to seal qualification for Russia as a tribute to captain Seamus Coleman - who suffered a serious injury earlier in the qualification process and is still sidelined.
“Of course, that was mentioned,” he said. “With Seamus being injured we wanted to get to the World Cup for him, he is a big miss and he is our captain and at the end of the day he is a great player. If you asked many of the lads they would probably want to do it for him.”