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Harry Kane was also on target at Deutsche Bank Park for Vincent Kompany's side, which moved four points clear at the summit after second-placed Borussia Dortmund drew with RB Leipzig earlier in the day.

Bayern hit the front from its first attack after just 15 seconds, with Serge Gnabry flashing the ball across the face of goal for a sliding Diaz to finish at the far post.

Kane's deflected header struck the crossbar soon after, but Eintracht thought it had equalised through Jean-Matteo Bahoya in the 15th minute, only to be denied after a video assistant referee (VAR) review with Ritsu Doan penalised for handball in the build-up.

The visitors capitalised on that let-off by doubling their lead after 27 minutes. Joshua Kimmich fizzed a pass into Diaz, who teed up Kane to drill beyond a helpless Kaua Santos.

Gnabry was narrowly off-target twice early in the second half, before the woodwork denied Kane once again in the 55th minute.

However, Bayern put the contest to bed six minutes from time. After a swift counter, Diaz wriggled free of Robin Koch before firing past Santos at his near post.

Kompany saluted Diaz after his brace.

"Considering this is his first season and his first steps in Germany, he's been impressive," the Bayern boss said.

"His activity and energy fit very well into the team. He's always involved, always there. He works very hard for the team.

"There's no pressure from me on Luis Díaz, I'm not asking him to do things the others are not doing. But as I said, his energy suits this team very well."

On the victory, the Bayern boss added: "We showed a good mix of stability and growing into the game. The first half was difficult, but it was okay. In the second half, we did many things right and created many chances.

"It was a very good performance against an opponent that we have a lot of respect for. We can be satisfied."

Bayern has won eight successive Bundesliga games for the first time under Kompany, while it has opened the season with 10 straight victories in all competitions for the first time since promotion to the Bundesliga in 1965.

Nevertheless, the head coach is not getting carried away.

"I try not to focus too much on the last 10 games," he added. "I don't want to focus on anything past the next game.

"The most important thing for me is that even if you lose one or two games – because it will happen – is that you have the feeling you can still win the next 10 games.

"We did something close to that last season, but what we've done now is proof that if we stay focused and keep going, then this could still happen in the future."

Kane, who became the first player to score 11 goals after the opening six matchdays of a Bundesliga season, concurred that Bayern cannot afford to relent.

"It was a great performance," the England captain said. "I thought, in the first half, we did well to be two goals up. In the second half, we were better and could've scored a couple more.

"We have momentum on our side right now, and we need to hold on to that."