Having failed to score in both of manager Michael O'Neill's previous matches, the goals finally came Wednesday night - Shane Ferguson and Paterson opening their international accounts and the returning Kyle Lafferty underlining his importance with his ninth senior strike.
Northern Ireland were playing for the first time in a new home kit bearing a design based on their 1980s glory days.
Expectations are a little lower than that now, but after O'Neill's tenure began with 3-0 and 6-0 defeats by Norway and Holland something positive was required here.
Another nod to the past came in the form of Olympiacos goalkeeper Roy Carroll, recalled in place of Lee Camp for his first start in six years.
Elsewhere, Chris Baird, Chris Brunt and Lafferty made their first appearances for O'Neill, having previously been unavailable.
Finland put together the first coherent move of the match, Roman and Alexei Eremenko linking well in midfield but unable to produce a final ball.
Northern Ireland's first chance resulted in the opener after seven minutes.
Rangers' Dean Shiels, attempting to prove he can combine life in the basement of Scottish football with a World Cup qualifying campaign, battled for the ball down the right channel and saw his deflected pass across goal fall for Ferguson.
The ball took a bounce off the Newcastle man, who then showed superb technique to lash home a powerful left-footed shot at the near post.
O'Neill, having previously drawn two blanks, looked visibly relieved in the technical area.
Finland almost produced a swift response but Craig Cathcart made a fine late challenge to dispossess Pukki.
With 19 minutes gone, the hosts were two ahead through Lafferty.
Again Shiels played his part, taking down Lee Hodson's lofted ball with the outside of his boot before whipping a cross into the six-yard area.
Lafferty battled to get the first touch and bundled over the line under pressure from Joona Toivio.
This time Finland were able to respond in kind, taking just three minutes before Kari Arkivuo's cross was expertly headed home by a straining Sparv.
Having pulled one back, the visitors drew level just two minutes later.
This time Northern Ireland were entirely to blame, Roman Eremenko doing the prompting and Brunt taking a loose ball on his chest before casually rolling the ball back into his own penalty area.
The back four were caught cold, leaving the waiting Pukki alone to roll his shot past Carroll via the post.
The quickfire double lifted the Finns who dictated the pace until the interval.
Njazi Kuqi was closest to adding to the scoring, curling right-footed just past the far post, while Brunt's speculative cross-shot was his side's best riposte.
O'Neill made two changes at the interval, Camp on for Carroll and Derby's Jamie Ward earning a second cap in place of Brunt.
Northern Ireland nearly began the second half with a goal, Ryan McGivern galloping down the left flank and picking out Shiels, who took a touch before pushing his shot across the face of goal.
The game continued to produce chances, Finland keeper Niki Maenpaa mis-kicking a hopeful long ball from Ward under pressure from Lafferty.
The Sion striker was first to react and quickly pulled the ball back for the onrushing Shiels, whose shot was smothered.
At the other end Toivio's 63rd-minute header may have struck a hand before being cleared by Ward on the post but Finland's penalty appeals were not upheld.
Substitute Riku Riski was close to putting his side in front for the first time in the 70th minute when he deftly lifted Toni Kolehmainen's pass beyond Camp and towards goal.
Fortunately for the hosts, Gareth McAuley was chasing back and able to flick the ball back away from danger.
Eight minutes later Finland did find their third, McGivern penalised for a foul 20 yards out and Hetemaj sending a rocket of a free-kick in off the upright.
The late penalty rescued O'Neill's side, Steven Davis surging towards the area and teeing up substitute Paterson.
The Burnley man went to ground without too much resistance but earned the penalty against Toivio nonetheless.
He took the spot-kick himself, drilling hard and low for his first goal in 14 caps.