Education Secretary Nadhim Zahawi denied Mr Johnson had broken any Covid rules by taking part in the festive activity.
Mr Zahawi spoke out after an image was published that shows the PM on a computer screen, sitting in front of a laptop in the Number 10 library, alongside two colleagues, one of whom is draped in tinsel.
Reports claim many staff who also took part and drank alcohol were huddled by computers in other Number 10 rooms.
The quiz took place on December 15 last year, three days before an alleged rule-breaking Christmas party in the building.
That event is currently being investigated by Cabinet Secretary Simon Case.
Downing Street said the PM “briefly took part virtually” to thank staff for their work during the pandemic.
Rallying around the PM, Mr Zahawi blamed “hype” created by the media for the parties row and said that “people can make their own mind up” about the photo, published by the Sunday Mirror, of the Christmas quiz.
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