Tim Tebow's older brother Peter performed a MIRACLE back in 2011 ... 'cause the guy was arrested for DUI, and his goose was seemingly cooked, but he somehow escaped with just a speeding ticket ... TMZ Sports has learned.
Here's what we know ... Peter Tebow was pulled over in Denver, CO at 1:43 AM on June 10, 2011 after cops say he was blazing through town -- going 90 MPH in a 45 while straddling two lanes of traffic.
When the cop approached the vehicle, he "observed that [Tebow's] eyes were bloodshot and watery, his speech was slurred and mumbled and his pupils were enlarged."
The officer asked Peter if he was on any medication, to which he replied ... "Yeah, I had some Percocet earlier. I had 2 pills in the morning and the afternoon."
He later stated, "I had 2 pills a couple hours ago."
In the report, the cop says he also smelled booze on Peter's breath ... but Peter refused to take both a road sobriety test AND a blood alcohol test.
Peter, who was 26 at the time, was eventually arrested and hauled to a nearby station where he was booked. He was later charged with reckless driving and DUI.
Now, here's where things get interesting ...
Despite the details from the arrest, Peter CAUGHT A HUUUUGE BREAK FROM THE COURT -- the DUI was dismissed outright and the reckless driving charge was reduced to a simple speeding ticket for going 20-24 mph over the limit.
His punishment -- $276 in fines (not including attorney's fees).
Fun Fact -- Peter's bro Tim was playing for the Denver Broncos at the time ... and Peter was reportedly living with him while attending seminary school.
We tried reaching out to Peter for comment -- nothing back yet.