Sub-zero temperatures at Dortmund's Signal Iduna Park did little to lift the match played in an eerie atmosphere, although Peter Stoeger's hosts did extend their unbeaten run to nine league matches.
There was near silence from the half-full south stand, which normally holds 24,500, as the club backed the supporters' silent protest.
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"We accept and respect that many spectators have stayed at home, we are against a further extension of the matchday and will bring the issue to the German Football League (DFL)," said stadium announcer Norbert Dickel before kick-off. "We are only for Monday games if there is a sporting reason."
The scenes in Dortmund came after Eintracht Frankfurt fans pelted the pitch with tennis balls against RB Leipzig last week in the first Monday game.
Bundesliga leaders Bayern Munich held by Hertha
Nevertheless, Germany star Reus had plenty to celebrate after claiming his second goal in only his third Bundesliga appearance since tearing a cruciate knee ligament in last May's German Cup final.
But the draw sees Dortmund stay a massive 19 points adrift of runaway leaders Bayern Munich in second place, after the defending champions had also dropped two points against Hertha Berlin on Saturday.
"It's annoying to end up with a draw after starting so well at home," bemoaned Dortmund midfielder Mario Goetze. "We didn't do enough with the ball we had and the performance wasn't what we had imagined. We're normally spoiled with the support we get from the south stand and we are looking forward to having that support once more when the stadium is full again."
Dortmund's opening goal on 16 minutes had 'Made in Germany' stamped all over it as three international team-mates combined.
A lightening counter-attack from their own goal covered the length of the pitch in a matter of seconds.
Goetze, who scored the winner in the 2014 World Cup final, slipped the ball to Andre Schuerrle, who had supplied the key cross in Rio de Janeiro four years ago.
Schuerrle's delivery to the far post in Dortmund was cut out by Augsburg's Martin Hinteregger, but Reus, who started the breakaway, continued his run and tapped home the loose ball.
Having dominated the first half, Dortmund rode their luck in the second and Augsburg grew in confidence.
Michy Batshuayi, on loan from Chelsea, had an off night having scored five goals in his five previous Dortmund games since replacing Pierre-Emerick Aubameyang.
After Brazilian midfielder Caiuby went close on multiple occasions, mid-table Augsburg deservedly drew level on 73 minutes.
Kevin Danso escaped his marker at a corner and powered a header at Dortmund goalkeeper Roman Buerki, who could only parry back to the Austria international.
Danso needed no second invitation and tucked home his second goal of the season on the rebound from close range.
The draw means Dortmund remain unbeaten in the Bundesliga since Stoeger replaced Peter Bosz as head coach in December.
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