Helped by holing a 51-foot eagle putt at the 16th in the final round, Australian ace Leishman claimed his second PGA Tour title in a thrilling conclusion at Bay Hill.
He carded a closing 69 for an 11-under-par 277 total, finishing a shot ahead of American duo Kevin Kisner (73) and Charley Hoffman (73), with McIlroy, who signed off with a 69, a shot further back alongside Tyrrell Hatton (71).
Leishman’s success secured his place in the Masters in a fortnight’s time, having come into the event sitting 61st in the world rankings but now jumping to 32nd.
“It’s amazing,” said the 33-year-old, who lost out to Zach Johnson in a play-off in The Open at St Andrews in 2015, the same year his wife, Audrey, was seriously ill with toxic shock syndrome.
“It’s been quite a while (his previous success came in the 2012 Travelers Championship) and my son keeps reminding me - daddy why don’t you ever win the trophy?
“I’ve been trying extra hard for him and it was great today that he was here and a special day with everything honouring Mr Palmer.”
Instead of a traditional blue blazer, the winner this year received a red cardigan sweater that Palmer favoured.
“You always want to win to honour the greats and it’s a special year this year,” added Leishman.
“It would have been great if he was up there standing on the back of the green but to win at his place is a dream come true.”
Having been four over par after two holes of his second round and still finding himself five off the lead heading into the final round, it was a brilliant effort from McIlroy to get in the mix down the stretch.
“I thought going out today if I could shoot anything in the 60s it would be a good score,” said the four-time major winner.
“Obviously I was trying to shoot a couple lower than that but overall played well, I’m really pleased with how I went this weekend and can take a lot of positives from it.”
His consolation is jumping above Jason Day into second spot in the world rankings, which see Russell Knox retain 21st position.
Martin Laird, who finished joint-49th at Bay Hill on three-over after a closing 71, is up three spots to 108th.
Swede Anna Nordqvist was a popular winner of the LPGA’s Bank of Hope Founders Cup in Arizona, where she enjoyed a successful college career.
The 29-year-old secured her seventh LPGA Tour triumph after a closing 68 for a 25-under-par 263 total at the Wildfire Golf Club in Phoenix saw her finish two shots clear of the field.
“Of all my wins, this is probably going to be the one that’s the most special,” said Nordqvist after claiming a top prize worth $225,000.
“If it wasn’t for me getting an opportunity to come to Arizona State University about 10 years ago, I wouldn’t be here today. This truly still feels like home, even though I’m based in Florida.
“I wasn’t even going to play (here) a couple of weeks ago and just ended up adding it at the last minute, so maybe it was meant to be.”
Stacy Lewis, South Korea’s Chun In-gee and Thai Ariya Jutanugarn finished in a three-way tie for second, with three more South Koreans - Park In-bee, Jang Ha-na and Ryu So-yeon - two shots further back.
Edinburgh-based American Beth Allen finished joint-31st after closing with a 72 for a 15-under total. The effort earned her just under $11,000.
A bogey at the last cost Steve Stricker his chance of a winning Champions Tour debut as former Open champion Tom Lehman won the Tucson Conquistadores Classic.
Lehman secured his 10th victory on the over-50s circuit with a final-round 66, finishing a shot ahead of Stricker (70) on 20-under-par.
for his 10th PGA TOUR Champions victory.
Stricker, who’d shot to the top of the leaderboard with a second-round 63, was trying to become the 19th player to win in his first start on the Champions Toyr and first since Miguel Angel Jimenez in 2014.
“It was a good positive week as I did a lot of good things,” he insisted despite that last-hole disappointment.
Kylie Henry headed off on her belated honeymoon on the back of third top-20 finish in a row on the Ladies European Tour, where she is starting to reproduce the form that earned two wins in quick succession in 2014.
On a Korean-dominated leaderboard - Hae Rym Kim beat compatriot Seon Woo Bae in a play-off to claim the title - the 30-year-old Scot ended up in 13th spot in the World Ladies Championship at Mission Hills in China.
On the back of opening rounds of 69 and 70, Henry had headed into the final round looking to add to her two title triumphs but, after a closing 74 that was a real mixed bag, she ended up seven shots adrift.
Nonetheless, it was another encouraging peformance for the Glaswegian, who ended her 2016 campaign by tying for 10th in the Omega Dubai Ladies Masters before starting the new one with a share of 18th in the Oates Vic Open.
Vikki Laing, the only other Scot to make the cut in a tri-sanctioned event between the LET, CLPGA and KLPGA Tours, finished joint-62nd on seven-over after a closing 78.
Grant Forrest maintained his solid start to the season in the first round of the MENA Tour’s Royal Golf Mohammedia Open in Morocco.
The 23-year-old carded a one-over-par 72, matching efforts from both Jack McDonald and Jamie Savage, on a tough scoring day at Royal Golf D’Anfa.
As Englishman Lee Corfield set the pace with a 66, recent Qualifying School winner Jack Doherty had to settle for a 77.
Clarke Lutton (73), Danny Kay (74) and Daniel Hendry (77) are the other Scots in the field for the second leg of Moroccan double-header.
Jeff Wright (Forres) is the new North of Scotland Alliance champion after claiming the crown for the first time at Inverness.
He beat the host club’s Bruce Thomson at the third hole in a play-off after the pair had carded matching one-under-par 68s in the Highlands capital.