Switzerland, who finished second in their qualifying group despite winning nine of their 10 games, drawn against Northern Ireland
Italy 'shouldn't be afraid of anyone' after drawing against Sweden in World Cup play-off
Four-time winners Italy will play Sweden in a play-off for a place in the 2018 World Cup while the Republic of Ireland take on Denmark, following the draw on Tuesday.
Northern Ireland will tackle Switzerland and Croatia and Greece will contest the other two-legged Europe zone play-offs to be played between November 9 and November 14.
Veteran goalkeeper Gianluigi Buffon's Italy, who were seeded for the draw in Zurich, will travel to Sweden for the first leg of their tie as they seek a ticket to Russia.
Gabriele Oriali, the Italy team manager who attended the draw in place of coach Gian Piero Ventura, said: "I think it could have been better. But we accept this draw. We are Italy and we shouldn't be afraid of anyone.
"Sweden are a very strong team, who qualified in a difficult group. They beat France and eliminated the Netherlands.
"We have optimism and history [on our side]. Imagine a World Cup without Italy."
The Italians were condemned to the play-offs after finishing runners-up to Spain in their qualifying group, but they have not missed a World Cup finals since 1958.
Sweden manager Janne Andersson said he expected "two tough games".
"But it would have been the same with other countries. I'm happy we know now. Now we can start work," he told Sky Sports News.
Northern Ireland manager Michael O'Neill conceded he faced an uphill task against the Swiss as he bids to steer his country to the finals for the first time since 1986.
The Northern Irish will play at home in the first leg.
"Switzerland had a great campaign though their group was one of the easiest. Our job is to make their life as difficult as possible," O'Neill said. "Having played Germany twice in the group it will set us up nicely for the match.
"Our aim is to take a lead to Switzerland and we had seven clean sheets in our qualifiers so we need a tight five when we go there."
The Republic of Ireland need to keep up the form they showed at the end of qualifying when they eliminated Wales to reach the playoffs, their coach Martin O'Neill said.
They have the advantage of hosting Denmark in the second leg.
"We have momentum and that's important," O'Neill said. "We won the last two games to get here. I'm now concerned with the next couple of weeks and making sure my players don't get injuries at club level."
Croatia will host surprise Euro 2004 winners Greece in the first leg of their play-off.
Croatia's manager Zlatko Dalic said the tie would be "a difficult job", but added: "I'm optimistic."