Slovakia topped Group B thanks to a late consolation goal against Sweden, which gave them a better goal difference in the head-to-head tiebreaker with Finland and the Swedes, after they all finished on six points.
The competition format - where rankings after the preliminary round came down to group placing, points, and goal difference - meant consolation or empty-net goals often decided who teams would face in the playoffs and quarter-finals.
Defending champions Finland's thrashing of Italy meant they took the final automatic quarter-final place, while Sweden's six points put them seventh overall and will face Latvia in the Playoffs.
Sweden have a roster full of NHL players, but have not overly impressed, struggling to overcome hosts Italy and losing 4-1 to their rivals Finland, while Latvia ended bottom of Group C after Denmark leapfrogged them with a late empty-net goal in a 4-2 win on Sunday.
The winner between Sweden and Latvia will face the USA in the Quarter-finals, while Canada will meet either Denmark or the Czech Republic.
Switzerland's runner-up spot behind Canada in Group A, after an overtime win over the Czechs, earned them fifth place in the rankings and a meeting with hosts Italy who finished bottom. The winner will face Finland in the last eight.
The Finns, with 24 NHL players in their 25-man roster, looked off the pace in their opener, going down 4-1 to Slovakia, but recovered to beat the Swedes before they hammered Italy.
Germany ended with three points, but the runners-up spot in Group C lifted them to sixth overall and they will be expected to overcome France in the playoffs to earn a meeting with Slovakia, bronze medallists in 2022.
Men's Qualification Playoffs
Tuesday 17th February (all times CET)
Czech Republic vs Denmark (16:40)
Canada vs USA Final awaits?
A mouth-watering final between Canada and the United States is still on the cards after the Group Stage of the men's Olympic ice hockey tournament.
NHL players returned to the Games after a 12-year absence, raising expectations that the North American rivals would contest the gold medal match for the first time since 2010, and the pair duly topped the rankings when the group stage wrapped up on Sunday.
Canada and the US were the only sides to end on maximum points, but the Canadians' better goal difference - bolstered by a 10-2 thumping of France - means they topped the rankings, while Slovakia and Finland also advanced to the last eight.
The winners of each of the three preliminary groups and the next best overall team automatically made the quarter-finals, with the remaining teams competing in a single-elimination qualification playoff.
