Victory ensures the Gunners finish top of Group B with one game - atripto Dundalk next Thursday - left to play and head into Sunday's north London derby against Tottenham, live on Sky Sports, on a high.
The only thing to spoil their evening was an injury to captain John Terry that saw the centre-half limp off before half-time and leave him as a doubt for Tuesday's tripto play Paris St-Germain in the first leg of their last-16 Champions League
Atletico were just about worthy winners of a typically tense and tight derby, although Real felt they should have been awarded a penalty in the second half for atrip by Atleti captain Gabi on Danilo.
But it fell to Isco to break the deadlock after the hour and Bale made sure 13 minutes from time, moving Madrid two points behind city rivals Atletico in second ahead of their tripto Athletic Bilbao later on Saturday.