Less than two minutes had been played when Salah smashed in his spot-kick after Moussa Sissoko had been penalised for handball in the area.
A disappointing final never truly got going after that, but Liverpool will not care, as they saw Alisson Becker make several confident saves in the latter stages before substitute Origi drilled in the killer second in the 87th minute.
That led to an explosion of joy from their supporters inside the Metropolitano Stadium as Jürgen Klopp's side made up for their defeat in last year's final against Real Madrid.
Salah has his redemption after injury ruined his night against Real in Kiev, and the revered Klopp has his first trophy as Liverpool manager, three and a half years on from his arrival at the club.
The victory means Liverpool have their sixth European Cup, further cementing their status as one of football's most storied clubs. They now have more trophies than Barcelona or Bayern Munich in the competition.
The stage was set for this match, only the second all-English final, but after all the hype and the stories of fans paying thousands for tickets for a game they simply could not miss, this was a strangely subdued affair between the two goals.
Perhaps the stakes were simply too high, or perhaps the three-week break since the end of the Premier League season was to blame.
Most likely the suffocating heat impacted on the players and prevented this from being like a typical Premier League clash.
It might also have been a result of the opening goal coming so early, badly affecting Tottenham's confidence.
Liverpool will not care and their fans will celebrate their moment of glory long into the Madrid night.