Referee Damir Skomina pointed to the spot with not even 30 seconds played at Estadio Metropolitano after Moussa Sissoko handled Sadio Mane's cross, and Salah thundered his spot-kick past Spurs goalkeeper Hugo Lloris.
With Tottenham threatening a late equaliser, Origi, on as a second-half substitute for Roberto Firmino, slammed in a loose ball from an 87th-minute corner to send the travelling Reds into raptures.
Check out the best photos from an amazing night in Spain in our gallery below...