Oscar broke the deadlock for Chelsea on the stroke of half-time with a fine finish into the bottom corner after being played in by Frank Lampard.
The Brazilian struck the crossbar with a wonderful effort early in the second period and there were also chances for Eden Hazard and Branislav Ivanovic, but Chelsea never looked fully in control and they were pegged back in the 71st minute by a curling shot from Mohamed Salah.
Basel were not content to hold on for a point, though, and were rewarded for their adventure eight minutes from time when Marco Streller's near-post header from a corner crept past Petr Cech and ruined Mourinho's big European return.
Willian was brought into the starting XI for his debut after arriving from Anzhi Makhachkala and there were also starts for Samuel Eto'o and Marco van Ginkel as Mourinho took charge of Chelsea in the Champions League for the first time since the draw with Rosenborg exactly six years ago which marked the end of his first spell at the helm.
Chelsea, missing the guile of Juan Mata, were unable to unlock the Swiss defence in a ponderous opening.
Willian had some promising touches and an Oscar corner had Yann Sommer flapping, only for the goalkeeper to be granted a free-kick.
Chelsea's first real effort on goal came after 26 minutes, when Eto'o turned Fabian Schar and found Eden Hazard, who blasted over from the edge of the area.
Basel were playing with men behind the ball but fired a warning on the break when Salah cut inside and shot over.
But Chelsea opened the scoring in the 45th minute when David Luiz, who scored in both legs of the sides' meeting earlier this year in the Europa League, found Lampard, who in turn fed Oscar. The Brazil forward's right-footed strike across goal nestled into the bottom corner to give the hosts a half-time advantage they barely deserved.
Oscar struck the bar with a curling effort early in the second period as Chelsea, prompted by Mourinho's interval intervention, began the second period with more purpose.
Ivanovic headed straight at Sommer from a Lampard corner and Hazard drilled over when he should have hit the target after being found by Oscar.
Mourinho introduced Mata for Willian with 23 minutes remaining, but soon after Basel equalised.
Gaps were appearing in the Blues' defence and Behrang Safari, wearing a head bandage following an earlier clash with Willian, found Streller with a diagonal pass and the target man laid the ball off for Salah to clinically net across goal.
Mourinho replaced Van Ginkel and Lampard with John Obi Mikel and Demba Ba, the latter going up front alongside the ineffective Eto'o.
Chelsea's pursuit of all three points left them exposed and Streller won a corner.
From the set-piece Streller evaded the attentions of Eto'o and Cahill to head substitute Matias Delgado's corner in at the near post. Cech might have done better, too.
Marcelo Diaz had an effort blocked as Basel looked for a third, with Chelsea well beaten as their winless run was extended to four games.