Elsewhere, Hamburg finally got their season up and running with a 2-1 win over Stuttgart, while Bayern Munich cast a huge doubt over Bayer Leverkusen's title credentials with a comfortable 3-0 victory.
Wolfsburg also managed a 1-0 triumph over Kaiserslautern despite playing the whole second half with ten men, while Schalke put four past Freiburg.
We look at the eleven players who impressed the most over the weekend.
GK: Simon Jentzsch (Augsburg)
Newly-promoted Augsburg are expected to face a tough battle against relegation for much of this season, which is why points like the one they earned in the 0-0 draw against high-flying Hannover are going to be extremely crucial.
And they had Jentzsch to thank for the point they got on Sunday, after he twice kept Hannover at bay with brilliant saves. His first was to keep out Jan Schlaudraff's blistering long-range strike, before he denied Lars Stindl from grabbing a late equaliser four minutes from time.
RB: Lukasz Piszczek (Borussia Dortmund)
On a weekend where it was imperative for Dortmund to win if they were keep their hopes of retaining their title alive, Mainz looked set to play the role of party-pooper for 90 minutes with their resolute defending.
But with the scores tied at 1-1 as the game entered injury time, Mario Gotze's free-kick was punched away into the path of Piszczek, who could not have picked a more important occasion to net his first Dortmund goal with what was virtually the last kick of the game.
CB: Alexander Madlung (Wolfsburg)
Another historical Bundesliga giant that has faltered in recent seasons, Wolfsburg notched their third win of the season with a hard-fought 1-0 win over Kaiserslautern. Yet things could have been so different when Sotirios Kyrgiakos received his marching orders seconds before half-time.
Instead, despite their numerical advantage, Kaiserslautern failed to find a way past the Wolfsburg defence, with Madlung standing firmly in their way. He was unbeatable in the air and put his body on the line on numerous occasions, as Wolfsburg held on for a win which came courtesy of Ashkan Dejagah's 63rd-minute effort.
CB: Daniel van Buyten (Bayern Munich)
Bayern's impressive start to the season continued on Saturday with a 3-0 win over title rivals Bayer Leverkusen. And while Van Buyten has been relegated to a reserve role in recent weeks, he made the most of his opportunity on the weekend by showing coach Jupp Heynckes what he's capable of.
A competent showing at the back was capped off with a brilliant free-kick in the 19th minute, with his powerful drive beating Bernd Leno all hands up.
LB: Jeffrey Bruma (Hamburg)
Hamburg finally kickstarted their season on Friday evening with a 2-1 victory over Stuttgart, although things were certainly looking bleak during half-time.
Trailing to Martin Harnik's 18th-minute strike, Hamburg made the most of a corner they earned six minutes into the restart when the on-loan Bruma showed why he is rated so highly at parent club Chelsea by nodding home Gokhan Tore's cross.
RM: Jefferson Farfan (Schalke)
Linked with a move away from the Veltins-Arena earlier this season, Farfan showed why Schalke were so keen on keeping him by scoring one goal and setting up another in the 4-2 win over Freiburg.
Farfan showed good awareness in the 33rd minute when he rose highest to nod in Raul's looping shot, before his blistering effort was too hot to handle for Freiburg custodian Oliver Baumann, who duly spilled the ball for Lewis Holtby to tuck home.
CM: Jose Manuel Jurado (Schalke)
Another played who impressed in Schalke's 4-2 win over Freiburg was playmaker Jurado, who was the engineer-in-chief behind many of his side's best moves on Saturday.
The highlight of his game came fifteen minutes from time, when his delightful over-the-top ball found Raul, who chested the ball down and blasted past Baumann in the Freiburg goal.
CM: Mario Gotze (Borussia Dortmund)
Playing in his first game since missing the last two through suspension, Gotze showed he could just turn out to be the catalyst to revive Dortmund's season, after pulling the strings in a hard-earned 2-1 win over Mainz.
While it was Ivan Perisic and Piszczek who got the goals that sealed the victory, Gotze was the one who regularly led the charge forward with his tidy passing and incisive running. Having already put in a delicious cross that Robert Lewandowski almost nodded home, the 19-year-old then whipped in a dangerous free-kick in injury time which led to Piszczek's winner.
LM: Gokhan Tore (Hamburg)
Unlike his on-loan team-mate Bruma, Tore was one player deemed to have no future at Chelsea, and was allowed to leave for Hamburg on a permanent deal earlier this summer.
However, based on Friday's performance against Stuttgart, allowing Tore to leave could just come back to haunt the Stamford Bridge hierarchy, after the Turkish international put in a masterclass performance. He constantly tormented the Stuttgart defence with his skillful dribbling, and was the architect for both Hamburg goals, twice whipping in pinpoint corners for Bruma and Robert Tesche to tuck home.
ST: Thomas Muller (Bayern Munich)
The young Bayern forward showed why he is regarded as one of the hottest prospects in European football with another accomplished performance in Bayern's 3-0 triumph over Leverkusen.
In a match that many tipped to be a close encounter, Muller ensured Bayern got off to the best possible start by giving his side the lead in the fifth minute, after good work down the flank by Franck Ribery. The German international led the line well for his team, and can now be regarded as one of Bayern's most important players.
ST: Lukas Podolski (Cologne)
For the second week running, Podolski showed why he's regarded as Cologne's talisman with an outstanding performance against Hoffenheim.
The German international laid on Cologne's opener for Mato Jajalo in the 20th minute, before bagging one of his own in the 64th minute when he ran onto Christian Eichner's long ball and faked a pass, before hammering a left-footed shot inside the near post.