The Colombian striker made the starting lineup due to the absence of first-choice forward Pierre-Emerick Aubameyang for a personal matter, with Dortmund struggling early in the first half and Alfred Finnbogason putting the hosts ahead.
Dortmund, who will face former coach Juergen Klopp's Liverpool in the Europa League last eight, levelled on the stroke of halftime with Armenian Henrikh Mkhitaryan starting and completing a lightning-quick move in the box.
Ramos came close twice early in the second half but did everything right in the 69th, controlling a 40-metre cross from Mats Hummels and laying it off for the trailing Gonzalo Castro to drill in.
The 30-year-old then got on the score sheet as well, forcing a point-blank save from keeper Alexander Manninger but tucking in the rebound in the 75th.
The result lifted Borussia to 64 points with Bayern on 69 following their 1-0 win at Cologne on Saturday.
Bayer Leverkusen battled back into European contention with a 2-0 victory at VfB Stuttgart to climb into sixth.
(Reporting by Karolos Grohmann; editing by Clare Fallon)
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