Leverkusen's late heroics 'hard to explain', says Alonso
Robert Andrich scored in the sixth minute of stoppage time, booting in a rebound from a Florian Wirtz free kick.
The goal extended Leverkusen's unbeaten run to 46 games in all competitions this season and to keep the Bundesliga champions on track to become the first side to finish a league season undefeated.
"I haven't seen that happen often in football. It's hard to explain," the 42-year-old manager told Sky.
Leverkusen have now scored 10 goals to win or equal matches in stoppage time this season.
Andrich's 96th minute goal was the second latest this season, after last Sunday's Josip Stanisic goal in the seventh minute of stoppage time which snared a 1-1 draw at Borussia Dortmund.
Alonso ran along the touchline to celebrate with his players last week but stood still and smiled this week after Robert Andrich's goal went in.
"Last week I got a little emotional, but this week I just could not believe we did it again."
Alonso's counterpart, Stuttgart manager Sebastian Hoeness, was disappointed the referee allowed the clock to run before Leverkusen's goal in a "hectic and very emotional" game.
"It was four minutes, then it was five minutes.
"In my view, the free kick should not have been allowed to happen."
Leverkusen started the season with just two major trophies in their history -- one German Cup and the Europa League.
Having broken through for the first league title in their 120-year history earlier in April, Alonso's side are on course for a remarkable treble.
Leverkusen face Roma in the Europa League semi-finals, with the first leg in the Italian capital on Thursday. Alonso's side have also made it to the German Cup final, where they will face second-division Kaiserslautern.