Australia, despite Head's 106, found runs hard to come by in a total of 283 for six that also featured Aaron Finch's 54.
Australia, for the second match in a row, following their 277 for nine in a 57-run tour-opening win over Sussex at Hove on Thursday, Australia failed to reach the now 50-over par total of 300.
But a target of 284 proved well beyond Middlesex, who were dismissed for 182 with nine overs to spare despite opener Max Holden's 71 that following a miserly one for 29 in 10 with his part-time off-spin.
Fast bowler Stanlake looked lively in taking two for 45, while Kane Richardson helped himself to some cheap dismissals as Middlesex lost their last six wickets for just 43 runs.
Head's hundred was his first at Lord's and he was delighted to get to three figures after not being at his best for county side Worcestershire in the early part of the season.
"I enjoyed getting back up the order, getting out there and having a hit," he told reporters.
"I felt like I've been in good form. I haven't got the runs I would have liked in the early part of the season for Worcester.
"It was a nice occasion, a nice place to get it a (hundred)."
Australia's overall batting was a concern, however, ahead of a five-match one-day international series against number-one ranked England, the 2019 World Cup hosts, that starts across London at The Oval on Wednesday.
It was also a reminder they were without two outstanding batsmen in former captain Steve Smith and his deputy David Warner, who both received year-long bans for their roles in a ball-tampering scandal during the third Test against South Africa in Cape Town in March.
In addition to Smith and Warner, Australia arrived in England without their injured frontline fast-bowling trio of Mitchell Starc, Pat Cummins and Josh Hazlewood, as well as sidelined all-rounder Mitchell Marsh.
But their white-ball problems predate the ball-tampering scandal, with Australia losing their last three bilateral ODI series -- against New Zealand, India and England.
D'Arcy Short (18) fell to a brilliant catch by Nathan Sowter -- born and educated in western Sydney -- at midwicket.
Shaun Marsh, playing his first match of the tour after Marcus Stoinis was left out following his hundred against Sussex, made 49 before he was caught at mid wicket by Middlesex captain Steven Finn, the England fast bowler, to give Holden a first List A wicket.
As at Hove, Glenn Maxwell fell in single figures to a spinner, the all-rounder lbw for three trying to sweep left-armer Ravi Patel on Saturday.
Head, though got his head down for a hundred. But the fact it took him 133 balls was evidence of Australia's struggles, despite an exceptionally short boundary on the Tavern Stand side of Lord's and soon afterwards he was caught behind off leg-spinner Sowter.
Australia's bowlers spared their batsmen's blushes, however.
Middlesex lost a trio of top-order wickets in quick succession and were 60 for three when Stanlake, in his first match of the tour, uprooted George Scott's middle stump.
But former England Under-19 captain Holden completed a run-a-ball fifty before falling to Stanlake.
"It was a great experience for all of us, playing against international opposition," said Holden.
"Hopefully a few of us will make it (to full international level) one day and it's good to learn off them and see how they go about it."
First Published: June 10, 2018, 9:02 AM IST