He grew up in Wrocław where his parents were expelled from Vilnius after World War II. A goalkeeper, Tomaszewski is best remembered by some for his performance for Poland against England, in a qualifying match for the 1974 World Cup, which England needed to win. Tomaszewski had been labelled "a clown" by Brian Clough before the match (the two men however became quite friendly in later years), but had the last laugh as he turned in a man-of-the-match performance repeatedly denying England's attackers; the only goal he conceded being an equalizing penalty from Allan Clarke. Earlier, Jan Domarski had scored for the Poles. Poland drew the game 1–1 and qualified for the finals in West Germany at the expense of England.
In "The Story of the World Cup", Brian Glanville wrote: "In retrospect, to be eliminated by so fine a side as Poland seems no disgrace, but this is a posteriori reasoning. I doubt if England could have made so dazzling a contribution as Poland to the tournament, yet it should be remembered that the Poland which beat England and the Poland which took their place were two very different propositions". (p. 191, 2005 edn.)
Poland went on to claim third place during a tournament in which Tomaszewski saved two penalties in two different matches (from Staffan Tapper and Uli Hoeneß) – the first 'keeper in FIFA World Cup history to do so. Tomaszewski went on to win a silver medal with Poland at the 1976 Summer Olympics, and also played in the 1978 World Cup, where Poland disappointed in only managing to get as far as the second group phase.
Tomaszewski's club career was mainly at ŁKS Łódź, having been forbidden by Poland's communist government to play abroad before the age of 30, even after coming to international attention.
After the 1978 World Cup, he moved abroad, first to Belgian club Beerschot, and then Hércules in Spain, before retiring in 1982. In all he won 63 caps for Poland, making him his country's most-capped 'keeper.