French Connection (1971; Best Picture winner, BTW). Gene Hackman is a cop chasing a suspect who's hijacked an elevated train. Hackman follows the car on the roads under the train. What this chase added to the movie car chase vocabulary is the front-bumper point of view. This adds to the sense of speed and the scene's frenetic energy.
And Hackman's reaction shots add a lot. Unlike the unflappable Steve McQueen in Bullitt, Hackman is flappable. Very,very flappable indeed. The best part is the baby carriage sequence about 1:12 in, which is edited at a frantic pace that was really rare in 1971 -- seven cuts in about six seconds, I make it. It works really well.
I couldn't find the whole chase, except for one version with background music added, so this is just a clip. It includes the best parts though. What it leaves out, though, is that Hackman commandeered the car from a random civilian. It's not even his own car that he's demolishing! Enjoy.