The Northern Ireland striker also took time to mark the death of the club's chairman in August 2007.
"I would like to dedicate this to David Crawford who passed away this season. I know how much of a Blueman he was," said Thompson.
"And to my grandfather who also died during the season. He was a big Linfield fan too."
Linfield manager David Jeffrey heaped praise on Thompson after the match.
"What can you say about Peter Thompson? It is all about how players perform and Peter was absolutely magnificent," said boss Jeffrey.
"These players simply do not know when they are beaten. They are a special bunch of people.
"Coleraine had been by far the better side in the first half."