And he looked to be heading for more frustration as Aleksandar Dragovic made amends for his first-half own goal by taking advantage of keeper Asmir Begovic's error from a corner to equalise with only 13 minutes left.
Chelsea's fans - who noisily supported Mourinho throughout - may have feared the worst but Willian responded in style with a spectacular 25-yard free-kick six minutes later.
The win moved the Blues into second place in Group G, three points behind leaders Porto but now with a two-point cushion to Dynamo Kiev.