A 12th-minute own goal which rebounded off Ivan Marcano under pressure from Diego Costa and a well-worked second-half strike from Brazilian Willian ensured victory for the struggling English champions and sent Porto into the Europa League.
Chelsea, cheered by a beaming owner Roman Abramovich, looked a completely different team from the one that has slumped to eight domestic defeats in 15 league games, including four at home.
The result took the pressure off Mourinho after intense speculation that the coach, who has won the Champions League with both Porto and Inter Milan, might lose his job if Chelsea failed to qualify for the knockout stages.
Saturday's 1-0 capitulation at home to promoted Bournemouth and Wednesday's lively and assured performance at the same ground were a Jekyll and Hyde transformation.
Chelsea looked composed from the start and when Belgian forward Eden Hazard served Costa a perfectly-weighted pass in the 12th minute, Iker Casillas in the Porto goal could only parry the Spain striker's shot.
The ball rebounded off Porto defender Marcano and into the goal.
Chelsea began to play with more freedom and it paid off when a speedy passing move between Costa and Hazard in the 52nd minute found Brazilian Willian, who cracked a shot inside the near post beyond the diving Casillas.
With Dynamo Kiev winning in the group's other game, Porto needed to attack and Thibaut Courtois had to keep out strikes from Yacine Brahimi and Cristian Tello.
TURNING POINT
A relieved crowd celebrated a possible turning point in a turbulent season by chanting Mourinho's name.
Mourinho's future has been the subject of speculation after his team, so masterly last season, slumped to 14th in the Premier league and look unlikely to reach the top four and a Champions League place for next season.
But the players showed their old passing precision and defensive solidity to tame a Porto side who have lost only one game this season -- to Dynamo Kiev in the Champions League last month.
The Portuguese team tested Courtois but the keeper and his defence held firm in a way they have failed to do in the Premier League.
Chelsea grew in stature as time ran out for the Portuguese, who looked short of the form they showed when they beat the London side 2-1 in Portugal in September.
Costa, top scorer last season but serially embroiled in controversy this season, earned a yellow card for stepping on Casillas early in the first half.
But he then proved a constant threat, testing Porto’s experienced Spanish goalkeeper to re-ignite a rivalry dating from their time at opposing Madrid sides Real and Atletico.
Oscar had a clipped shot expertly saved by Casillas and Hazard hit the post with 10 minutes to go as Chelsea sought a third goal.
(Reporting by Clare Lovell, Editing by Ian Chadband)
