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Florian Niederlechner met Mads Pedersen's low cross to give Augsburg a flying start inside the first minute of the match, giving Dortmund cold sweats from the memory of conceding at exactly the same time on the opening day of last season.

But as was the case back then — it recovered to beat RB Leipzig 4-1 — Dortmund again turned things around and went on a scoring spree in front of its home fans to make the most of Bayern Munich's inability to win its opening game against Hertha Berlin on Saturday (AEST).

Alcacer started the scoring little more than two minutes after Dortmund had gone behind, Jadon Sancho sending Marco Reus to the byline from where he pulled the ball back for the Spaniard to tap in. Six of his 20 Bundesliga goals have now been scored against Augsburg.

Julian Weigl and Mats Hummels both tested Tomas Koubek in the Augsburg goal and Alcacer missed the target, before Reus twice found Koubek a bridge too far as Dortmund laboured to find a breakthrough before half-time.

While the second began with far less incident than the first, it wasn't long before the home fans were again on their feet.

In the 52nd minute, Axel Witsel sent the ball low across the face of goal to England international Sancho, who drilled a low effort in off the far post.

Koubek had kept Augsburg in the game in the first half, but fell apart in the second, a fumble allowing Alcacer to tee up Reus to double Dortmund's lead.

There was nothing Koubek could do to prevent Alcacer from hammering in a fourth just a minute later as the hosts turned the screw, and with the result in the bag, Dortmund was able to ease up in the closing stages.

But there was still enough time and appetite to allow Julian Brandt to open his account for his new club, a calm left-foot volley from Witsel's pinpoint cross beating Koubek easily.