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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.