First five eighths Aiden Morgan kicked the goal to tie the game 3-3.
More breakdown ill-discipline from Wellington saw McClutchie restore the three-point lead with a penalty goal on the quarter-hour mark.
Magpies captain Tom Parsons was penalised for offside in his 100th first class game, allowing Morgan to level the scores once more.
Both teams had opportunities in each others' red zones but were halted by tenacious defence as the clock ticked over half an hour.
A scrum penalty against Wellington allowed McClutchie to nudge Hawke's Bay back in front with his third penalty goal just before halftime.
Magpies prop Joe 'Apikotoa, playing against his former province, received a yellow card for a no-arms tackle on Lions hooker Asafo Aumua.
The resulting penalty let Morgan make it 9-9 at the break.
Wellington jumped straight out of the blocks scoring the game's first try a minute into the second half.
Loose forward Peter Lakai opened up the Magpies' defence with a pick-and-go and sent TJ Perenara in to score.
'Apikotoa returned from the sin bin with Wellington hot on attack.
When Hawke's Bay were penalised at the breakdown 10 metres short of the tryline, Morgan kicked his fourth penalty goal in the 52nd minute.
The game and the Ranfurly Shield looked to be slipping away from the Magpies before they won a scrum penalty on the hour mark and launched a lineout drive inside the 22 metre line.
But Lions lock Dominic Bird, a Hawke's Bay native, forced a knock on and Wellington cleared their lines.
Lincoln McClutchie prevented a certain Lions try when he booted the ball dead in-goal before Julian Savea could get his hands to it.
The former All Black winger was pinged for holding on with ten minutes to play and McClutchie nailed the penalty goal to make it a one-score game.
Magpies centre Nick Grigg was penalised for not rolling away inside Hawke's Bay's 22 metre line, but Aiden Morgan missed his first kick of the game with four minutes remaining.
Hawke's Bay won a midfield penalty for holding on just before the hooter sounded so threw to an attacking lineout on the 22 metre line.
TJ Perenara received a yellow card for cynically slowing the Magpies ball down and they kicked to another five metre lineout.
But Wellington held tight to take the win and the Ranfurly Shield.
Hawke's Bay's next game is against Bay of Plenty in Tauranga on Saturday, with a win looming as crucial to earning a home quarterfinal.
Hawke's Bay 12 (McClutchie 4/4 pens)
Wellington 19 (Perenara try; Morgan 4/5 pens, 1 con)
HT: 9-9
