The young Greek striker went on as a second-half substitute at Oxford and wasted little time in making a big impact.
His two cool finishes, both after good work by Harry Howell, delighted Albion fans who have been keen to see what both he and Charalampos Kostoulas can do.
Both Danny Welbeck and Georginio Rutter were rested for the second-round tie.
Albion will now weigh up the next move with the likelihood seeming to be that Tzimas will be on the bench against Manchester City on Sunday.
Head coach Fabian Hurzeler said: “There are different demands in a Premier League game than the game today.
“He came into a game where it was already 3-0 so it’s not the intensity you can expect in a Premier League game.
“For sure he’s closer with the step today but I’m not sure if he might be an option for the weekend, we have to see how he reacts.
“But it’s positive. It’s step by step, it’s not like going all-in from the start. It’s giving him a step and then the next step, that he can adapt and he has a positive feeling.
“He showed today that it’s very important for him that he scores goals because he was quite happy in the locker room.
“That’s a really good step and we have to be not that euphoric, we have to be very patient with him and let’s see what will be the next step.”
Tommy Watson also introduced himself to fans with a super finish, curling into the top corner.
He could also offer a wing option among the subs when City visit as competition for the places in the matchday 20 hots up.