Arsenal grabs upset win at Dortmund
Dortmund had come into the Group F encounter searching for an eighth successive home Champions League win and had never lost against English opposition.
Jurgen Klopp's well-drilled side, who had won 2-1 in London a fortnight ago, dominated for long spells, but were made to pay for not converting their chances when Ramsey nodded home a knockdown from Olivier Giroud on 62 minutes.
It may not have been the flowing display which manager Arsene Wenger would have preferred - but the Barclays Premier League leaders once again answered questions with a display of real character to hand a rare defeat to last season's beaten finalists.
With Napoli beating Marseille, Arsenal still have work to do to secure safe passage through to the knockout stages, but will have gained more belief they can last the distance this season.
Arsenal had come into the tie on the back of a 2-0 victory over Liverpool which moved them five points clear at the top of the table.
The Gunners were also unbeaten in 14 away matches in all competitions since recording a famous win at Bayern Munich in March.
Dortmund, though, dominated the first half and were left counting the cost of not making the most of that spell in control, where the English side could not muster any attack of note and Henrikh Mkhitaryan missed a great chance for Dortmund when he shot wide from the edge of the penalty area after Arsenal were carved open down the right.
Gunners goalkeeper Wojciech Szczesny saved well from Jakub Blaszczykowski following the restart, before Ramsey secured what proved to be the winner just after the hour for his 11th goal of the season.
The Associated Press was used in this report.