The world champions, who lost 2-0 to Poland in their previous Group D fixture on Saturday, appeared to have put a below-par first-half display behind them when Toni Kroos netted a 71st-minute opener.
Yet Ireland, confident following wins in their opening two qualifiers, stunned their more illustrious hosts deep into second-half stoppage-time.
Jeff Hendrick sent a searching cross from fellow substitute Wes Hoolahan back across goal and John O'Shea - earning his 100th cap - showed excellent anticipation to direct the ball low into the bottom-right corner to the delight of the travelling support.
Ireland are now level with Poland on seven points at the top of the group - three ahead of Germany and Scotland.
Having claimed a famous victory over Germany on Saturday, Poland were unable to maintain that momentum but managed to pick up a hard-fought 2-2 draw against Scotland in Warsaw.
The home fans had barely finished celebrating the win against their neighbours when Krzysztof Maczynski fired in off the right-hand post after 12 minutes, but Shaun Maloney brought them back down to earth with a bump when he struck six minutes later.
Scotland went ahead against the run of play thanks to Steven Naismith's finish from a James Morrison free-kick, but Arkadiusz Milik - a thorn in the side of the Scottish defence throughout the second half and a scorer against Germany three days earlier - pulled Poland level with a sublime strike 14 minutes from time.
Georgia triumphed 3-0 in Gibraltar in the group's remaining fixture.
In Group I, Cristiano Ronaldo scored in injury-time to earn Portugal their first points of the campaign in a 1-0 win at Denmark, while the match between Serbia and Albania was abandoned.
Referee Martin Atkinson was forced to bring proceedings to a halt four minutes before half-time in Belgrade, with the score at 0-0, when a drone flew over the pitch carrying a flag featuring Albanian national symbols.
Serbia defender Stefan Mitrovic jumped to bring the flag down, sparking scuffles between players from both sides, while a number of supporters also entered the field of play as an unsavoury melee escalated.
Riot police subsequently surrounded the pitch after the players had been taken from the field and the match was duly called off.
Northern Ireland maintained their 100 per cent start in Group F with a 2-0 win in Greece and sit two points clear of Romania, who beat 10-man Finland 2-0.
Hungary edged a 1-0 win in the Faroe Islands, while Switzerland triumphed 4-0 at San Marino in Tuesday's only Group E fixture.
