Keeper Handscomb's aerobatic catch to dismiss Cam Green also ensured the division-two clash at Bristol was a pretty miserable one for the star allrounder, whose latest bid to prove his form before the World Test Championship final fell flat.
There was a thrilling third-day finale to a low-scoring contest on Sunday as the Australian contingent were all at the heart of the visitors' two-wicket win.
Gloucester had hoped Bancroft and Green could deliver them to a challenging second-innings total but the skipper's three-hour, 141-ball vigil was ended when he was trapped lbw by Dutch international Logan van Beek for 43.
Then Green, who'd scored a century in his first match after being signed up by a mystery county benefactor, was caught behind off namesake Ben Green for just two to go with his first-innings four.
Handscomb flung himself full-length to his left to make the wonderful grab as Gloucester then went on to make just 152, leaving Leicestershire 143 to win.
Brilliant bowling from Dominic Goodman (4-33) had the visitors on the rack but Handscomb steadied the ship with his stubborn 96-minute knock of 26 and aided by wicketkeeper Ben Cox's 47 and a stubborn unbeaten 15 by No.9 Green, the visitors just prevailed to go top of the second division.
At Trent Bridge, Nottinghamshire bade a fond farewell to their short-term Australian import Fergus O'Neill, who departed after his four-match stint as the leading wicket-taker in the country.
The Victoria quick took his bow with 3-74 in the second innings against Sussex, taking his season's tally to 21 and helping them to a nine-wicket win that puts them top of the first division.
"Fergie's been outstanding, can't talk too highly of him," said Notts captain Haseeb Hameed.
"For a 24-year-old to come in for his first overseas stint and do what he's done is outstanding, and the biggest thing I can say about him is that he became a leader in the group very quickly.
"You just had to watch him field yesterday, let along the 20-odd overs he bowled, to see he's got a massive heart."
Evidently, Notts want him to return. "Hopefully, we can build a few more memories together in the future," said Hameed.
Surrey have moved ominously into top gear as the champions bowled out Somerset for just 119 before wrapping up an eight-wicket win at The Oval.
Dan Worrall looked back on song with his 3-16 off nine overs, a performance that will have been noted with interest by selectors who could this summer thrust the one-time Australia international into the England Test side.
They'll have doubtless particularly enjoyed his splendidly over-the-top, zig-zagging celebration after dismissing Tom Banton caught-and-bowled.
