Chi-squared for continuous variables
It sounds like the chi-squared test confirms your suspicions about age being correlated with the response.

As far as I am aware, the null-hypothesis for the chi-squared test is "there is no relationship" between the two variables. The test statistic is calculated based on the assumption that all observations are evenly distributed amongst the cells in the contingency table, so the test should work for most kinds of relationships.

A word of warning - the test is sensitive to data imbalances.