Miyoshi, a 40th-minute replacement for the injured Ethan Laird, volleyed his first Blues goal in spectacular fashion deep into first half stoppage time. And Jutkiewicz settled the outcome six minutes from time with a close-range finish, shortly after being sent on for Keshi Anderson.
Bristol had centre-back Rob Dickie sent off for a second yellow card after 75 minutes and could have no complaints, even though Nahki Wells missed a great chance to level.
Blues boss Eustace said: "It was an outstanding effort by the whole group, but it's important not to get carried away.
"Miyoshi came off the bench against Leeds was really exciting. Again he showed what an important player he is going be for us.
"He was out for nine months before joining us, so we have to be careful how we manage him. But his talent is there.
Denne historien er fra August 20, 2023-utgaven av The Football League Paper.
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Denne historien er fra August 20, 2023-utgaven av The Football League Paper.
Start din 7-dagers gratis prøveperiode på Magzter GOLD for å få tilgang til tusenvis av utvalgte premiumhistorier og 9000+ magasiner og aviser.
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LUKE BOOSTED BY WALES ACE LIAM
Swans bid to mark new era in style...
MATT'S DELIGHT OVER RECORD
WYCOMBE boss Wanderers Matt Bloomfield hailed his history-makers after victory at Lincoln City.
TON-UP IAN ENJOYS HIS SPECIAL WIN
AN Evatt described his 100th win as Bolton boss as very special, although he needed Aaron Collins' injurytime goal to bring up the three figures.
DONS LACK A CLINICAL EDGE AS SADDLERS GRAB POINTS
NATHAN Lowe's strike inspired promotion-chasing Walsall to victory over AFC Wimbledon at the Cherry Red Records Stadium.
SUB GRIMES IS IN-SPIRED TO HEAD THE WINNER
CAPTAIN Jamie Grimes headed in a late winner for Chesterfield after a game of very few chances appeared destined to remain goalless.`
COBBLERS TEST IN TROPHY FOR POSH
HOLDERS Peterborough United have been drawn against fellow League One side Northampton Town in the Round of 32 of the newly-named Vertu Trophy.
HORNETS REMINDED OF GRAY'S BRILLIANCE
WAYNE Rooney expressed his delight as Plymouth extended their unbeaten league home run to six after Andre Gray's last-gasp leveller.
MARTI DOUBTING JOB AFTER DRAW
Rangers home run continues
BIG MAC'S ON TARGET TO SEE OFF THE TIGERS
LUTON boss Rob Edwards felt it was a very good day at the office as his team turned in a gritty performance to beat Hull.
Rohl confident Owls
DANNY Rohl said getting results is the only thing missing as his Owls were held at home by Cardiff.