Harness, who netted 10 in all competitions last term, scored his first goal of the season in the 2-0 win against the Railwaymen, with his 64th-minute strike adding to John Marquis’ opener just after half-time.
And it was Tunnicliffe who claimed the assist as his delicate through ball put the winger in.
That was the midfielder’s second of the game – following his contribution to Marquis’ opener – and his third of the season after his role in Lee Brown’s winner at Fleetwood last weekend.
Yet the 28-year-old is known for his goalscoring exploits.
Last season he registered just two for Luton, which is one less than his previous best – the three he scored for Millwall during their 2018-19 Championship campaign.
That hasn’t stopped the Blues boss, however, setting him and Harness a lofty return for the season ahead – 12 each.
Speaking to BBC Solent after the final whistle against Crewe, Cowley lauded his side’s second goal.
It was an effort initiated by debutant goalkeeper Gavin Bazunu – and provided Harness with the platform to reach his target for the term.
Cowley said: ‘I thought the second goal was a lovely goal for us.
‘It’s not often the goalkeeper gets an assist, but he plays so high, Gavin.
‘He’s so brave with his positioning that that allows us to swing the ball and use him, which allows us to get an extra number up the pitch – and it was played outside their shape and then played back inside their shape.
‘And I’m pleased for Marcus because him and Tunni, I’ve got them down for 12 goals each, so that’s one for Marcus anyway and I thought Tunni was excellent today, I thought he was the best player on the pitch.’
Harness’ goal against Crewe took his goal tally for the Blues to 20, with his 10 last season his best return to date in a Pompey shirt.
Last term, Tom Naylor was the Fratton Park club’s top goalscorer from midfield, with eight goals to his name.
Andy Cannon followed with just the two.