The striker scored an incredible free-kick after three minutes to give Manchester United an early lead in their first game without Jose Mourinho.
Woodward sacked Mourinho on Tuesday morning and hired the Norwegian to take over until the end of the season.
And the vice-chairman appeared to be proud of his decision after United broke the deadlock.
As the United team celebrated, the cameras caught Woodward cheekily grinning in the stands.
Fans on Twitter could not believe his response, with one stating: "Woodward with a wry smile. Haha. What a goal."
While another said: "Ed Woodward with a smile on his face."
And he was given another reason to smile when Ander Herrera doubled United's tally after 29 minutes.
But Solskjaer's afternoon got off to a shaky start after he was booed when he got off the team coach in Cardiff.
And Paul Pogba was also given a rapturous reception on his return to the starting line-up.
The £96m star was axed by Mourinho for the crunch clash with Liverpool – which turned out to be his last in charge of the club.
But there was no sign of any resentment from the sell-out travelling support in South Wales when the players went through a warm-up in front of them.
As the players made their way over, the Reds supporters broke out into cheers for the first time and Pogba made a point of spending time acknowledging them.
The fans responded by passionately greeting him with fist pumping and a not a jeer could be hard – proof Pogba is still very much in their good books.
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