The first of the two-legged tie will be held at Windsor Park, where Northern Ireland recorded seven clean sheets from their 10 qualifiers.
The Swiss won all but one of their qualifying fixtures, losing to Portugal and missing out on automatic qualification for Russia.
O’Neill acknowledged the Swiss will be difficult to beat but he believes his side are in with a chance over the two legs.
Speaking to Sky Sports News, O’Neill said: “We’re pleased with the draw, particularly to miss Italy and Croatia.
“Switzerland will be a difficult opponent but I do believe it’s an opponent we can overcome. The first leg at home, hopefully we can have a positive result to take to Switzerland.
“Sometimes you get the benefit of an away goal when you play the second leg away. It’s a game we’re very capable of winning over 180 minutes.
“We have to manage the game carefully at home. The key is to make sure you’re in the tie as long as possible. The aim is certainly to take a lead to Switzerland.
“Possibly you’d have preferred it the other way around, but you don’t get everything. We’ve been formidable in Belfast and we have to put on another performance like we have done over the last four years.”
The first leg is due to be played between 9 and 11 November with the return leg in Switzerland held between November 12 and 14.
Switzerland sit 11th in the FIFA world rankings but O’Neill is hoping his opponents will feel deflated after missing out on an automatic spot despite such a strong qualifying campaign.
“I think to be honest their group was probably the easiest, but hopefully they’re maybe, mentally, a little bit disappointed having led the group from start to finish, to miss out on the automatic place and now face a play-off,” O’Neill said.
“Our job is to make that as difficult as possible and I’m certain we’ll do that.”
Following Scotland’s dismissal of Gordon Strachan, the Northern Ireland boss has been touted for the vacant post but he insists his focus is firmly on getting to Russia.
“I haven’t even given any thought to that,” O’Neill added.
“My focus has been on this draw and will be on Switzerland and getting us to the first World Cup in 30-odd years.”
