Real had their own injury blow with right-back Dani Carvajal having to go off, replaced by Nacho in the 37th, and ended the half with Benzema's effort being disallowed for offside after Cristiano Ronaldo's header was saved by Karius.
Bale directed a looping overhead scissor-kick high into the Liverpool goal in the 64th minute after Liverpool's Sadio Mane pounced from close range in the 55th minute to equalise an earlier Karim Benzema goal.
Ronaldo has won the Champions League for the fifth time in his career. The best I have been doing is to come on and make an impact, I certainly did.
Mo Salah's 2018 World Cup could be in doubt after being substituted in the Champions League final. Five minutes later he made way for Adam Lallana.
Three minutes into the second-half Isco struck the crossbar when he should have scored but the breakthrough came in the 51st minute in unfortunate circumstances for Liverpool goalkeeper Karius.More news: Korean leaders meet to salvage Trump-Kim summit
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But it was an even quieter night for Mohamed Salah, with the Liverpool forward lasting only 30 minutes before being forced off with a shoulder injury that now threatens his participation at the World Cup with Egypt.
But the Egyptian FA tweeted that Salah had his X-ray, showing he had a "sprain in the shoulder ligaments" and that it was "optimistic" he would be fit for the Russian Federation tournament, which starts on 14 June.
It didn't take Liverpool long to get back on level terms.
But their renewed hope was crushed upon the introduction of Bale.
Such a strike deserved to be the victor, although it was his long-range shot that beat the embarrassed Karius in the 83rd minute that made sure of the victory. If he hits the net against Liverpool on Saturday in Kiev, he will become the first ever player to score in four European Cup finals.