A performance lacking in urgency, ambition and imagination was punished by the livewire Egyptian late on as the Swiss side completed a famous double over the Blues.
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 it repeated the feat courtesy of Salah's dramatic late winner.
Murat Yakin's side now heads into its final group game against Schalke next month knowing it only need a points to progress to the last 16.
Chelsea was poor on the night and failed to register a single shot on target, but Schalke's failure to beat Steaua Bucharest ensured its progress.
Willian replaced Eden Hazard in the only change to the Chelsea side that beat West Ham 3-0 at the weekend, while striker Fernando Torres was back on the bench after missing the weekend match with an injury.
Goalkeeper Yann Sommer, midfielder Salah and defender Ivan Ivanov all returned to the Basel starting line-up.
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.
John Obi Mikel then cleared off the line after Ivanov got a toe to a Fabian Schar corner and Salah was twice denied by the busy Cech as Chelsea remained on the back foot.
There was a blow for the visitors three minutes before halftime when Samuel Eto'o was carried off, with Torres replacing him.
Hazard replaced the ineffective Oscar nine minutes into the second half as Chelsea struggled to get going.
The replacements provided more of an attacking threat and Mourinho's men were far more solid at the back after the break.
Ramires should have done better when he was played in on the right 12 minutes from the whistle, but the Brazil midfielder lacked composure.
Basel snatched its crucial winner when Salah raced away following Schar's pass, and he kept his nerve with a clinical finish to stun Chelsea.