Our on-loan midfielder played the full 90 minutes at Toyota Park, having made his debut off the bench in last weekend’s 2-0 defeat at Columbus Crew.
A penalty from Jeff Larentowicz on 68 minutes put Fire in front, but Galaxy equalised six minutes later through former Everton loanee Landon Donovan.
Ex-Spur Robbie Keane played the full game in attack for Galaxy.
Grant tweeted after the game: “Good to get my first 90mins in a few months today, fans were great, felt we should have got the 3 points!”
Fire visit Colorado Rapids on Thursday.