The 39-year-old came on as a late replacement and claimed Exeter's final score in their 33-9 victory at Sandy Park.
The Kiwi powered over from close range to claim his second score of the season and ensure the Chiefs maintained their unbeaten record in the Premiership at home this season.
"That was for the boys," Budgen said after the match. "I told my wife [Tina] and my son [Dylan] that I would try and do something today.
"We had the boys' funerals on Thursday and the one promise I made was that I would try and score for them, so when I got that ball today there was no way I was going to stop."
He added: "I'm pretty happy I went over at the end, I don't mind coming on for the odd five minute burst. It was a good result for us, but we're a little disappointed not to get the bonus point."
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