Thomas Mueller scored two goals and Bayern Munich rallied to rout Stuttgart 6-1 despite leaving the most expensive player in Bundesliga history on the bench for most of the match on Sunday.
Javi Martinez watched as Bayern scored three goals inside the first six minutes of the second half, then came on in the 77th for his Bundesliga debut.
By then, Stuttgart was down to 10 men following the ejection of Vedad Ibisevic in the 74th.
Martinez signed for Bayern this week on a Bundesliga record C40 million ($50 million) transfer from Athletic Bilbao.
The emphatic win left Bayern atop the standings on goal difference over Eintracht Frankfurt, the only other team to start the season with two wins.
Two-time defending champion Borussia Dortmund dropped points in a 1-1 draw at Nuremberg on Saturday.
Stuttgart got off to a promising start when Martin Harnik's left-foot shot from inside the penalty box rattled Bayern's crossbar in the fourth minute.
But Harnik drilled home a stunning volley at the far post from a free kick by Arthur Boka in the 25th. Manuel Neuer got his palm on the ball but could not keep it from slamming into the roof of the net.
In between Harnik's chance and goal, Luiz Gustavo shot wide from the edge of the penalty area.
Mueller equalized in the 32nd when he connected with a cross from Mario Mandzukic. Sven Ulreich blocked his volley but Mueller followed through and put the rebound in.
Only a minute later, Kroos blasted home from the edge of the box after Shinji Okazaki had lost the ball in Stuttgart's half.
Gustavo got his goal in the 43rd, driving home from 30 metres with a tremendous shot into the right corner.
Bayern, playing without ill Arjen Robben, intensified the pressure after the break. Another loss of possession, this time by Gotoku Sakai, led to Mandzukic's goal in the 47th.
In the 49th, Mueller notched his second after a fast break left five Bayern players against two Stuttgart players and only two minutes later Bastian Schweinsteiger headed in the sixth as Stuttgart's defence disintegrated.
Ibisevic was sent off for an altercation with Jerome Boateng, who received a yellow.
"We reacted very well after falling behind 1-0," said Schweinsteiger, who has been seeking his form after several injury setbacks last season. "For the first time since February my body feels healthy."
Earlier, Artur Sobiech scored two goals and Szabolcs Huszti set up all four as Hannover thrashed Wolfsburg 4-0 away.
Hannover finished the match with 10 men but all the goals had been scored before Robin Knoche was sent off in the 65th.
Karim Haggui and Sobiech scored before halftime and Leon Andreasen and Sobiech added two more after the break for Hannover's first win of the season in the league.
Haggui's glancing header from a corner in the 10th minute put Hannover ahead.
Hannover doubled the lead in the 26th. Josue lost possession in midfield and Hannover outplayed Wolfsburg's defence with a fast counterattack finished by Sobiech.
Adreasen put the match out of reach for Wolfsburg when he headed in a free kick from Huszti at the near post in the 53nd.
Four minutes later, the unmarked Sobiech headed in a perfectly timed cross from Huszti.
Things only got worse for Wolfsburg when Knoche was sent off for his second booking of the match — after he had come on only at the start of the second half.
Before the match, midfielder Ashkan Dejagah was given an official farewell from the fans. Dejagah left Wolfsburg for Fulham.