Kuopio's Nigerian striker Aniekpeno Udoh got in front of Bratislava's goalkeeper Greif and had no trouble scoring from close range after a low pass from the right side.
Dominic Dale, the world number 70, also reached Stage Two after topping his group with two wins and one draw.
It was short-lived joy for the hosts though, as Hoffenheim had the last laugh when Kramaric unleashed a 15-meter hammer to snatch the 3-2 win in injury-time.
Thomas Tuchel's side welcomed back goalkeeper Keylor Navas, defender Marquinhos and forward Mauro Icardi after the trio were among seven players tested positive for COVID-19, but missed Kylian Mbappe, who is still in self-quarantine at home.
But there was no place for striker Edinson Cavani, who has yet to find a new club after parting ways with Paris Saint-Germain in June. The 33-year-old has not played since March.
Jozwiak started his senior career for Lech Poznan in 2016 after coming through he club's youth academy. He made 104 appearances and scored 15 goals during his spell with Poznan from 2016 to 2020, including a brief loan to GKS Katowice in 2017. Enditem
"We surprised Al-Taawoun with our physical presence which gave us the upper hand," said Resan.
Talavera's return to the international fold comes after a series of impressive performances for Pumas UNAM, whom he joined from their Liga MX rivals Toluca in July.
"It [a return to international football] is a wish and a goal. I want to take it game-by-game and if the opportunity arrives I will be very happy. If it doesn't, I'll continue working hard so that I can be considered."
Club officials said the number of fans must be manageable.
The Championship League has been expanded to a full World Snooker Tour ranking event this season, featuring 128 players in three stages over 21 days.