Cory Monteith Death Report -- Injecting Heroin, Slamming Alcohol Before Death

Cory Monteith was shooting heroin and downing champagne in his hotel room on the night of his death ... this according to the final coroner's report obtained by TMZ.

The "Glee" star was discovered alone in his hotel room in Vancouver, Canada on July 13 shortly after noon.

When responders arrived to the scene, they discovered a "spoon with drug residue and a used hypodermic needle."

They also found 2 empty champagne bottles and glasses.

The coroner lists Monteith's official cause of death as "mixed drug toxicity, involving intravenous heroin use combined with the ingestion of alcohol."

The report also notes that Cory "had a history of illicit drug use with intermittent periods of rehabilitation and of abstinence from drugs."

The coroner suggests that Cory's tolerance for substance abuse may have been lower than usual because he had stopped using since a rehab stint in April.

Monteith was 31.