The Eygptian produced a clinical finish at the St. Jakob-Park on Tuesday to ensure the Swiss champions leapfrogged Schalke into second place in Group E, while Chelsea qualified despite the defeat.
Basel had ended the Premier League club's 29-match home unbeaten run in the group stages of the competition back in September with a shock 2-1 win at Stamford Bridge and they repeated the dose courtesy of Salah's dramatic late winner.
Murat Yakin's side now head into their final group game against Schalke next month knowing they only need a point to progress to the last 16.
Chelsea were poor on the night and failed to register a single shot on target, but Schalke's failure to beat Steaua Bucharest ensured they progress.
Chelsea manager Jose Mourinho warned Basel that his side were much improved since the Swiss champions' shock win at Stamford Bridge in September, but there was no evidence of that as the home side dominated the opening stages.
Petr Cech had to be alert to palm away a Taulant Xhaka free-kick from wide on the left after only two minutes and Chelsea failed to heed the warning when they backed off 10 minutes later and Fabian Frei's strike was saved by the Czech Republic goalkeeper.
There was a blow for the visitors three minutes before half-time when Samuel Eto'o was carried off, with Torres replacing him.
The Belgium winger and Torres provided more of an attacking threat and Mourinho's men were far more solid at the back after the break.
And Basel snatched a crucial winner when Salah raced away following Schar's pass, and he kept his nerve with a clinical finish to stun Chelsea.
