Alonso was handed his first start at Bayern a day after completing his transfer from Real Madrid and he watched ex-Borussia Dortmund striker Lewandowski open the scoring after 10 minutes in Gelsenkirchen.
Shortly before being substituted, the Spanish midfielder was involved when Schalke equalised on 62 minutes. Alonso attempted to execute a sliding goal-line clearance only to see the ball bounce into the net off Benedikt Hoewedes’ arm.
Despite Bayern’s protests, the goal stood and the home team comfortably held on to end a run of seven defeats in a row against the Bavarians.
“I thought the first 20-25 minutes were really good,” Bayern coach Pep Guardiola said. “In these games you have to keep possession and after 25 minutes we didn’t manage that. That was the problem.”
Bayern almost got the opening goal after only four minutes when Ralf Fahrmann saved from Thomas Mueller but Guardiola’s side did not have to wait much longer.
Sebastian Rode was the architect, playing a one-two with Lewandowski inside the penalty area to leave the Polish international with an easy finish.
A rash clearance from Bayern goalkeeper Manuel Neuer almost gifted Schalke an equaliser before half-time, but Schalke full-back Kaan Ayhan was unable to hit the unguarded goal from the halfway line.
Bayern seemed content to sit on their lead and Schalke eventually drew level when a Sidney Sam free-kick was poorly dealt with. Alonso did his best to prevent a header across goal finding the net and there was little Hoewedes could do to prevent the ball going in off his arm.
“We definitely didn’t come out of the starting blocks well,” Schalke 04 boss Jens Keller said. “But my team deserves great credit for the way they reacted to the early goal.”
– Two from two for Leverkusen –
The result meant that Bayer Leverkusen sit top of the Bundesliga after Roger Schmidt’s side came from behind twice to beat Hertha Berlin 4-2 earlier on Saturday.
Following an impressive win in Dortmund last week, Leverkusen made it two wins from two thanks to late goals from Julian Brandt and Karim Bellarabi.
“This was a very tough game for us and because of that it was very valuable,” Leverkusen manager Schmidt said.
“At half-time we saw it as a challenge to grow into such a game. In the end we deserved to win so hats off to my team.”
Tin Jedvaj turned into his own net as visitors Hertha took the lead in the first half but the Croatian defender made amends when he levelled on 50 minutes.
Hertha made it 2-1 on the hour when Julian Schieber nodded in his third goal of the campaign but two minutes later Emir Spahic headed home from a free-kick.
Brandt then smashed home with 16 minutes left after Bellarabi had struck the bar and Bellarabi rounded off the scoring with the best goal of the game.
Meanwhile, Paderborn earned their first ever win in the Bundesliga with an excellent 3-0 victory at Hamburg.
After 29 minutes, Elias Kachunga pounced on the rebound for his second goal in as many weeks. Mario Vrancic then intercepted a pass to double Paderborn’s advantage with 21 minutes left before Moritz Stoppelkamp added a third.
“Paderborn fully deserved to win,” Hamburg coach Mirko Slomka said. “Our performance, overall, was shocking for us – a bitter result. We’ve really disappointed our fans.”
Cologne also got their first victory since returning to the top flight by beating Stuttgart 2-0 thanks to first-half goals from forwards Yuya Osako and Anthony Ujah.
Hoffenheim were unable to keep pace with Leverkusen after they were pegged back in a 1-1 draw at Werder Bremen, while VfL Wolfsburg are still without a win after being held to a 2-2 draw by visitors Eintracht Frankfurt.
On Friday, Borussia Dortmund held off a late comeback to beat Augsburg 3-2 in what was their first league win of the new campaign.