The Italian giants nearly blew a huge lead against a determined Bonn but ultimately prevailed 86-76 and will now return home for Game 2 on Thursday.
Sharrod Ford scored 17 points, Reshawn Terry 16 and Keith Langford 14 for Virtus.
Ford and Terry grabbed seven rebounds apiece.
A blowout looked to be on the cards when Ford dunked and was fouled on the play midway through the third quarter. He sank the free throw to give the visitors a 61-39 advantage.
The 21-point lead proved not to be a stranglehold, though.
Earl Rowland, who scored a game-high 21 points, led the Germans in their comeback.
In an 8-0 run that cut the game to 61-47, he had six points including two jump shots and a dunk.
Bonn, sparked by a Johannes Strasser trey, then reeled off nine straight points to finish the third quarter and they trailed just 67-59.
John Bowler's three-ball reduced the arrears to 69-62 a minute into the fourth quarter.
Bowler and Rowland later made back-to-back lay-ups to make it 74-69 and force Virtus coach Matteo Boniciolli to call a timeout.
Immediately out of the timeout, Langford buried a three to settle the Virtus nerves and though Bonn twice more got to within five points, they fell to defeat.
Virtus out-rebounded Bonn 34-24 and they also made a living at the free throw line, sinking 22 of 25.
Bonn were just seven of 11 at the charity stripe.
Virtus also shot well from long range, making 10 of 21 while Bonn were seven of 17.