The lead swung five times in the first half as Will Witty and Ollie Devoto’s scores for the hosts were interspersed by Matt Cornish and Curtis Rona tries.
Tom Hendrickson’s try put the hosts ahead again on 50 minutes but Creevy restored the Irish advantage and dogged defence at the death kept the much-changed league leaders at bay.
The win for the Exiles ended a nine-match losing streak and was their first over Exeter since a 28-26 victory in Reading on January 11, 2015.
London Irish director of rugby Declan Kidney said: “I am really happy to have got a result. We didn’t spend as long in our own half as we have done in other matches, which means the opposition didn’t score as much and that gave us a chance towards the end.
“They want to win and that is something you cannot coach, that attitude. That is why I am glad they have got a return for it.
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