They maintained their perfect start to the qualifying group stage by winning 3-0 at home to Georgia.
Albion striker Tzimas started the game in the middle of a front three and sent a shot wide at 0-0.
He put Greece ahead from a first-half penalty and played until the 65th minute.
Tzimas has now scored in three successive games, including the away win over Germany, as the Greeks lead their group.
The next test comes at home to Northern Ireland in Livadeia on Tuesday.
Tzimas has made it clear he is keen to progress to the senior squad after seeing Albion colleague Charalampos Kostoulas make that step up in this window.
Kostoulas is with the squad preparing to play at home to Scotland.
Both Greek signings started the recent Carabao Cup tie at Arsenal and Kostoulas scored his first Premier League goal at Manchester United.
Meanwhile Tzimas has also been told he is now ready for the Prem.
Albion boss Fabian Hurzeler said recently: "He is physically more ready, he's adapting to the demands from the Premier League.
“He's doing well in training. He's getting better in possession, in understanding our style of play so it's just a mix of everything.”