The 2-1 win featured Larne captain Jeff Hughes cutting the gap in injury-time after a first-half goal double by Linfield that could ultimately lead to an end-of-season trophy double.
Healy’s Blues can now tackle Coleraine on Tuesday in a top-of-the-table Premiership clash bolstered by cup victory over Larne aware a single point would secure another league title triumph.
“We were outstanding tonight,” said Healy on BBC Sport NI. “It was important to get around a team like Larne.
“We started the game in the manner we wanted to finish the game.
“Larne are an outstanding club, they’ve been immense this year...but I just thought we were better tonight.
“Credit to these players...they get written off and myself as a manager - but I get a buzz off it.
“I’m immensely proud of the players tonight for the way they approached the game, played the game, managed the game and, eventually, won the game.
“I love the players, it’s disappointing when you have to leave good players on the bench or out of the squad.”
Preparations for the Sadler’s Peaky Blinder-sponsored showpiece final were disrupted by a protest lodged by Crusaders in the aftermath of a semi-final exit to Larne on Tuesday.
However, an IFA ruling yesterday morning left Linfield and Larne with a green light and Healy singled out his squad’s focus on the red-letter date in the blue riband trophy.
“The energy, the effort, the attitude, the application the players put in tonight - not only for me as manager but my staff,” he continued on BBC Sport NI. “My staff have been incredible - you play the semi-final on Tuesday so you’ve basically 48 hours to not only recover but assess.
“There was a lot of talk about the cup final going ahead and who you were going to play or whatever else but we were prepared...we got the right result.
“This should be a confident group of players - they’re so honest and so hard-working.”
Lavery broke the deadlock before Cooper grabbed a second before the break to set Healy and his Premiership leaders on course for a league-and-cup double.
Lavery’s pace created problems for Larne within the opening moments when, after three minutes, he raced in behind on to an upfield pass and managed to cut it back into the danger area.
The supporting Cameron Palmer met the loose ball in the box but Conor Mitchell raced off his line to produce the block.
However, Linfield’s corner-kick led to the opening goal seconds later as Niall Quinn’s curling delivery dropped in the heart of the box and the unmarked Lavery guided home from a few yards.
Larne’s response featured a growing grip on possession and playmaker Martin Donnelly almost took advantage of a loose touch by Jimmy Callacher but the Linfield centre-back recovered to block the threat.
The on-song Ronan Hale was presented with a first glimpse of goal after John Herron slipped the ball into the Larne striker inside the area, however, his shot on the turn lacked the power to trouble Chris Johns.
Mitchell raced out of his area on 20 minutes in a bid to beat Lavery to a ball forward and the Larne goalkeeper had his team-mate Albert Watson to thank for reading and reacting to the trouble to race across and clear.
Donnelly’s clever clipped pass lofted over the Linfield defence was then controlled on the run by Hale but Conor Pepper managed to block the shot.
Former Glenavon player Cooper added another moment to savour at Mourneview Park by gaining the ultimate reward for his run from deep on the half-hour mark with his current club’s second goal on the grand stage.
Pepper’s strong work along the right was capped by a cross across the face of goal beyond the under-pressure Lavery at the near post that Cooper slotted in at the back post despite the effort of a diving Mitchell.
Linfield managed to maintain the momentum despite the half-time interval and Mitchell was on hand at a stretch to claw away Lavery’s looping header after the dangerous Cooper whipped over a cross Quinn kept alive.
Larne, however, carved out two sights of goal in quick succession on 54 minutes.
Watson’s pass from deep was met by Larne substitute David McDaid and his drive forced Johns to show strong hands to stop the effort.
Seconds later a long-range drive by Fuad Sule had the Larne contingent within the 1,000-strong final fanbase up off the Lurgan seats but it proved just too high for the target.
Play settled into a disjointed period before Linfield regrouped for a strong finish designed to take advantage of the extra space as Larne pushed forward in search of a lifeline.
Cooper came close to adding his second on the scoresheet by showing pace to gain an edge over Watson but Mitchell was alert to close the angle.
Cooper managed to move past Watson again soon after but his attempt to square the ball to the unmarked substitute Christy Manzinga finished in disappointment with a Larne block.
Larne’s Hughes picked up a clearance on the edge of the box and fired goalwards but a Callacher block helped to protect the Blues’ clean sheet.
Hughes cut the gap with an injury-time consolation when the veteran scooped home from a few yards after a ball bounced around inside the packed penalty area.
However, Linfield had silverware confirmed seconds later with a 44th Irish Cup prize.
LARNE: C.Mitchell, Cosgrove, Watson, Robinson, Jarvis, Hughes, Sule, Herron, Donnelly (McDaid, 46), Lynch (Randall, 53), Hale (McMurray, 67).
Subs (not used): Kelly, Scott, A.Mitchell, Wade Slater.
LINFIELD: Johns, Pepper Haughey, Callacher, Clarke, Quinn, Palmer, Mulgrew, Millar, Cooper, Lavery (Manzinga, 74).
Subs (not used): Moore, Newberry, Stafford, Larkin, Nasseri, Stewart.
REFEREE: Andrew Davey.