The encounter began with plenty of passion from both sets of players, with very little time being allowed for anyone to settle on the ball.
An excellent run on the left from Roy McBain took him to the byline and Craig Dargo's header was captured by Derek Stillie after just six minutes.
At the other end a searing run by Craig Conway ended with a terrific shot crashing off the crossbar.
Stillie was then called into action when he held on to a Graham Bayne header originating from a Dargo corner.
After a relatively flat spell, John Rankin went close when he steered a low drive past the post.
Just before the interval, Caley Thistle thought they had taken the lead but Dargo was offside when Ross Tokely passed into the area for him.
Brewster made an early appearance in the second half from the bench in place of Mark Kerr, which added spice.
With both sides going all out for the winner, the clock ran down and they had to settle for a share of the spoils, although a last-gasp Barry Robson header for United was met by a top-drawer save from Mark Brown.