The St. Louis Blues' Stanley Cup run will HELP the city's baseball team ... so says Cardinals manager Mike Shildt, who tells TMZ Sports the hockey champs have "inspired" his guys!!!
Of course, nobody gave the Blues a chance to win Lord Stanley back when the season began ... but they improbably made their way through the league to hoist the trophy Wednesday.
When we got Shildt out in NYC just a couple days later ... he told us the Blues' season is motivating as hell -- and the Cardinals are definitely taking notice!