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.
"Congratulations to Bologna for this victory. We had our problems in the first half. We gave up big runs to Bologna. We respected them a little too much. In the second half we were on the same level. We cut two times a twenty point lead back to five points. We lost by ten but in this [playoff] series it is not important to win with one or ten points. That is what we will try to do in Bologna."
John Bowler (player Telekom Baskets Bonn):
"It will be very tough to go and win two games in Bologna. We saw that they are ready for us. We came out with too much respect. In Bologna we have to act more aggressive. I still believe that we can reach the Final Four."
Matteo Boniciolli (coach Virtus BolognaFiere):
"First of all congratulations to Telekom Baskets Bonn because they never gave up the game. I think that we deserved this victory because we controlled the game from the first second to the end. We knew Telekom Baskets Bonn are a good and very athletic team. Without Brandon Bowman they were missing one of their best players. We expect him to be back [for the] Thursday game. This [game] was only the first half of the series. I told my players now we have two chances to close [the series]. One of our goals this season is to participate in the EuroChallenge Final Four."
Sharrod Ford (player Virtus BolognaFiere):
"It was a really tough game. It was a must-win for us. We still have to win a second game. The series is definately not over yet. On Thursday we have to play like we did tonight."