VfB Stuttgart were still looking for their first win after coming from two goals behind to draw 2-2 at Werder Bremen while Borussia Monchengladbach drew 1-1 at Bayer Leverkusen in the day's other game.
Bremen's Assani Lukimya came on as an 89th minute substitute and contrived to get sent off less than two minutes later for a foul on Georg Niedermeier.
Stuttgart's Martin Harnik was also dismissed for a second yellow card.
Hoffenheim conceded 11 goals in losing their first three games and appeared to be on course for another unhappy afternoon when Matthieu Delpierre, under no real pressure, stooped to head Konstantin Rausch's low cross into his own goal at the near post in the 26th minute.
Junuzovic's compatriot Harnik pulled one back five minutes after the restart and Stuttgart grabbed only their second point in four games when Cacau diverted Niedermeier's shot into the net with nine minutes remaining.
In the other game, Patrick Hermann gave Gladbach an early lead, converting Juan Arango's 40-metre pass, but Michael Kadlec levelled after 12 minutes for Leverkusen. Andre Schuerrle missed a 70th-minute penalty for Leverkusen, striking his effort against the post.
