1989 Chevrolet Cavalier ELEcTRIcAL ?

I'd check the idle air system and clean the throttle body, go from there. How long since a tune-up? Check for applicable trouble codes. Your obd1 so you should be able to check codes, yourself. To check codes, use a jumper wire between the A & B terminals at the datalink connector, then turn key just till dash lites come on, no further. Then the mil on the dash starts flashing, you count the flashes to get the codes. Your looking for two digit codes.

Usually when using the brake the throttle is closed, if you open the throttle just a little, will it stay running?