England appeared likely to wrap up the Investec series with a second successive innings victory inside three days, after Sri Lanka were bowled out for 101 and asked to follow on 397 runs behind.
But half-centuries from their captain Angelo Mathews (80), opener Kaushal Silva (60) and Dinesh Chandimal (54no) made a mockery of their previous struggles as they closed on 309-5.
Finn’s solitary success, the wicket of Silva, came after he stirred himself up and found a little extra life in a docile pitch.
It was reward for a hard-working spell, and England’s collective efforts, as Sri Lanka at last produced a worthwhile rearguard after collapses here and at Headingley last week.
For Finn, there were signs he is beginning to find his feet again after a slow start to the summer for club and country on his return from a side injury.
“It’s no secret I’ve been searching for rhythm – it’s been there in patches,” he said.
“I wanted to smash the deck, to help with the rhythm.
“It’s hard to find something as a bowler that makes it click, when you are searching for it – maybe I’ve been doing that this summer, I’ve been desperate for form and rhythm.”
He has had to be patient, and was again – but tried to move up a gear by engaging in a battle, verbally at one point, with the batsman.
“I still feel I’m doing a job, but I haven’t been 100 per cent good 100 per cent of the time – which I was in South Africa and last summer.
“It helps take your thought process away from the pitch – if looking for rhythm you’re best doing that, getting yourself in a fight at the other end of the pitch, rather than at your own end.
“The umpires said don’t use any bad language – which I adhered to – (and I decided to) run in as hard as I can.”
England’s four-man pace attack could only chip their way through the Sri Lanka order.
“I came out after tea trying to get into a fight and have a bit more intent on a wicket where it’s not doing much for me on the length,” added Finn.
“Given my height, it can be a bit more uncomfortable.
“I worked it out for myself.
“Our mantra has been trying to starve them of runs, and it will bring wickets – not bowl jaffas every ball. That was the way I felt I could starve them of runs.”
Sri Lanka were a different proposition with the bat second time round, and Silva confirmed there had been an urgent discussion about how they must improve.
He said: “I wouldn’t say it was harsh words.
“It was just everyone knew what we are capable of.”
They are still likely to lose the series here today, however.
“We haven’t done extraordinarily well, but we have gone one step up. That is important,” the opener added.
“From the start of the second innings, we wanted to be positive.
“We showed that intent, even with the running between the wickets, being more aggressive.
“The problem is, if you play the ball in two minds, you end up getting out – so we’d rather be positive, even in defence.”