Meanwhile Harry Maguire's 500th minute header was the first goal Sweden had conceded since Tony Kroos' 95th minute winner for Germany 210 minutes previously.
Saturday's shootout was Croatia's second of this World Cup and the 500th World Cup tie to be decided on penalties since Schumacher's moment in Spain 36 years ago.
SAMARA, Russia, July 8 (Xinhua) -- The World Cup numbers game continues as eight teams became four after the quarterfinals of the World Cup with France, Belgium, England and Croatia progressing while Brazil, Uruguay, Sweden and the hosts, Russia, bowed out.
The game was also the first clean sheet the English have kept in this World Cup and their first in a World Cup knockout stage since 5006, when they beat Ecuador 1-0.
Schumacher was involved in the first ever World Cup tie to be decided on penalties as Germany beat France in the 1982 semifinals although he should have earlier been sent off for a notorious challenge on French forward Patrick Battiston.
Russia's exit on penalties to Croatia later on Saturday night was the third time a host nation has been eliminated from the World Cup on penalties, with the other victims being Mexico in 1986 and Italy, who lost at the semifinal stage in 1990.
England's 2-0 win over Sweden on Saturday means England have reached the semifinals for the third time: once in 1966, when they won the World Cup, once in 1990 and now here in Russia.
Part of the reason for Croatia's success was another stunning display from goalkeeper Danijel Subasic, who has now stopped four penalties in shootouts in this World Cup: only Argentina's Sergio Goycochea in 1990 has performed a similar feat, although German keeper Harald Schumacher saved a total of four shootout penalties in 1982 and 1986.