Italy, who last failed to qualify for the World Cup in 1958, will play the second leg at home on Nov. 13 in the most eye-catching of the four ties.
Switzerland, who finished second in their qualifying group despite winning nine of their 10 games, were drawn against Northern Ireland, who last qualified in 1986, with the first match in Belfast.
Croatia, who were runners-up behind Iceland in their group, will face Greece with the first leg at home.The fourth tie pits Ireland, who will be playing in a playoff for a major tournament for the ninth time, against Denmark, who would host the first match.
Sweden has not beaten Italy in their last five meetings, since a friendly in 1998, and the Italians won a dour game 1-0 at Euro 2016.
But the prospect of having their fate decided in a two-leg playoff, after finishing runners-up behind Spain in their group, has got the Italian media and public on edge.
“We will prepare for the challenge with faith and determination,” said Italy coach Gian Piero Ventura in a statement on the Italian federation’s website.
“Nobody has ever considered, or is considering, the hypothesis of not qualifying for the World Cup,” added Ventura, who did not attend the draw.
“The love of all Italians will accompany us. History teaches us that it is always this way in the do-or-die moments. We will all go to Russia together.”
Sweden coach Janne Andersson was confident.
“We had the toughest qualification group against Netherlands and against France and we played some really good games. If we can play at the level, then we can beat any team in the world, including Italy,” he told Reuters.
“We have a good mentality in the team, we have confidence.”
Northern Ireland coach Michael O’Neill, whose team includes a number of English second-tier players, said his side would make life as difficult as possible for Switzerland, who are bidding to qualify for their fourth successive World Cup.
“We’re here on merit. We were second in our group behind the Germans, of course, we can believe we can win it,” he said.
“We can make the tie very difficult for Switzerland. They will be favourites to go through, we believe we are capable of overcoming them.”
Ireland coach Martin O’Neill said: “I know Denmark and I know the manager Age Hareide, he and I used to play together so it will be an interesting confrontation.”
Croatia coach Zlatko Dalic will be taking charge of only his second and third games after he was appointed two days before their final group match against Ukraine.
“I respect Greece but I am convinced it’s down to how we perform,” he said. “The tricky bit is that we are playing the return leg away.”
World Cup playoff
Northern Ireland v Switzerland
Croatia v Greece
Denmark v Ireland
Sweden v Italy
Two-legged ties to be played Nov. 9-11 and Nov. 12-14