That was in 1999. Case won his first start, against Cleveland - a game that gave Brian Billick his first victory as Ravens head coach. The next week, the Ravens won again as Case threw a 54-yard touchdown pass to defeat Atlanta in overtime.
But two defeats followed, including a humbling loss to Kansas City on national TV in which Case threw for a couple of touchdowns - to the other team. That night, he completed 15 of 37 passes for 103 yards.
End of Stoney. Case closed.
Relegated to backup duty, he signed with Detroit at season's end.
Now 35, Case plays in the Arena Football League, starting last year for Tampa Bay before being sidelined with a shoulder separation. "I may play for another year or two," he said. "I have the rest of my life to do something else."
Case, who is single, lives in Phoenix and enjoys golfing, water-skiing and hunting elk in New Mexico. It's a somewhat carefree life for a man who appeared in only 24 NFL games.
"I played six years in that league and invested my money well," he said. "Whatever I make now in the AFL is icing on the cake."
His fondest memory of Baltimore? Maybe the crabs.
"Every restaurant I went to in that city, if the owner recognized me, he'd bring out his signature crab dish," Case said. "That was cool."
His worst recollection? The dreadful 35-8 loss to Kansas City.
"I know that game hurt my career because everyone watched it," Case said. "A lot of coaches have told me that that game sticks in their minds.
"I did make mistakes that night, but everyone did. I hit, like, one of my first 11 passes - and I was on the ground 11 times. No excuse, I was missing guys, but I was getting beat up, too.
"It's hard to throw from your back, it really is."
• With the Ravens: 1999.
• Other teams: Arizona Cardinals, 1995-98; Indianapolis Colts, 1999; Detroit Lions, 2000; San Jose (AFL), 2006; Tampa Bay (AFL), 2004-05, 2007.
• Current job: Quarterback for Tampa Bay Storm of the Arena Football League.
• Career statistics: (NFL) -- 163 completions in 318 attempts for 1,826 yards, 4 TDs and 15 interceptions; 60 carries for 270 yards and 5 TDs. (AFL) -- 53 completions in 81 attempts for 581 yards, 9 TDs and 2 interceptions.
• Fun fact No. 1: Named for fictional TV character Stoney Burke, a rodeo rider on 1962 series of the same name.
• Fun fact No. 2: Member of the Odessa-Permian (Texas) High School team chronicled in the book, movie and TV series Friday Night Lights.
• College: New Mexico, where he was first NCAA player ever to pass for 8,000 yards and rush for 1,000 in his career.