The Brazil forward, who is one of the few players who cannot be blamed for Chelsea's season of struggle, struck a curling free kick to earn a 2-1 win over Dynamo Kiev and enhance the Blues' hopes of progression from UEFA Champions League Group G.
Chelsea's second win in six games came amid a cacophony of support for Mourinho, who was the subject of the first managerial vote of confidence of Roman Abramovich's 12-year ownership on 5 October.
The caveat was that results must improve but the defeat of Dynamo and a favourable fixture list - after Sunday's tricky Premier League clash at Stoke City - has done much to boost morale at Stamford Bridge.
"Confidence is coming for us and the results are coming as well," Willian told chelseafc.com.
"We have to keep going and keep fighting on the pitch. We lost some games and it's been difficult for us but we are trying to play better.
"We know we have to improve more and keep going in the same way."
Mourinho was overjoyed by the backing of the Blues support, something which was in little doubt after successes in two spells which included the Premier League and Capital One Cup double last season.
The 52-year-old Portuguese signed a new four-year contract, until June 2019, on the eve of the Premier League season and his agent Jorge Mendes does not expect Chelsea to dispense with his services, despite six defeats in 11 Premier League games.
Mendes told BBC Sport: "He doesn't need to prove anything to anybody.
"He knows what to do. Many people are saying these things but there is no chance (he will leave). He will solve the problem. He is the best.
"The reaction from the supporters tells you everything. They like him.
"Everyone - players, coaches - you have good moments and bad moments. It is impossible to find someone like him to solve the problem."
Stoke ended Chelsea's League Cup defence on penalties last month and Mourinho will know the Premier League is where the results really matter, despite Wednesday's win putting the Blues in pole position to advance to the last 16 with Porto.
Chelsea next play at Maccabi Tel-Aviv on 24 November and Porto at home on 9 December.
Their run of fixtures after the trip to Britannia Stadium, for which Mourinho is currently banned after his dismissal at West Ham United, and the international break looks like a fine opportunity to build momentum.
Chelsea's Premier League opposition before the end of 2015 is Norwich City, Tottenham Hotspur, Bournemouth, Leicester City, Sunderland, Watford and Manchester United.
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