The Leith clash was a dress rehearsal for next month's William Hill Scottish Cup semi-final but it is the hosts who will have to brush up their act after being out-worked by their hungry city rivals.
Hearts rode across Edinburgh on a wave of optimism having claimed victory over Rangers on Saturday.
And they used that new-found self-confidence to hand Stendel his first set of back-to-back victories since the German took over three months ago with a display full of swagger.
Jack Ross' hosts did pull one back through Melker Hallberg late on.
Yet they were lucky not to find themselves down to 10-men as the officials missed Marc McNulty's blatant stamp on Clair.
But the Tynecastle midfielder showed no ill-effect as he stroked home a penalty just after half-time, while expert strikes from Bozanic and Washington sealed a stunning result to Hearts above fellow strugglers Hamilton.
The Jambos were without John Souttar after he was ruled out for the season with an Achilles injury and there was a fresh blow before kick-off when a knee injury limited skipper Steven Naismith to a seat on the bench, with Liam Boyce taking his place.
Hibernian were grateful the rough treatment meted out to Martin Boyle early on did no lasting damage to the winger.
Aaron Hickey, Clevid Dikamona and Bozanic all took turns to wipe out Boyle in the opening five minutes.
But it did not put the Australia international off his stride as he drove down the left before swinging over a vicious near-post cross which Christian Doidge could only flash wide with his head.
Then came the big flashpoint. McNulty looked to have ample time to avoid making contact with Clare as the Hearts midfielder stumbled to the ground yet still managed to plant his foot square into the Englishman's back.
Referee Kevin Clancy appeared to miss the incident but McNulty will not get away Scot-free and can expect a letter from Scottish Football Association compliance officer Clare Whyte in the coming days.
Hearts were desperate for the points to aid their fight for survival but saw two big opportunities go amiss as Ofir Marciano clawed away a Halkett header before Boyce nodded over.
But it would only take eight minutes of the second half for the visitors to grab the breakthrough they craved as Scott Allan was penalised for handling in the box.
In Allan's defence, his eyes were shut as a Bozanic delivery hit his dangling arm but this time Clancy saw the whole episode and immediately pointed to the spot, with Clare's low penalty just about evading Marcanio's reach down to the Israeli's right.
Hibs should have responded almost immediately but there were no takers to convert Paul Hanlon's knock-down from a Allan corner.
Instead Ross' team were masters of their own downfall as a catastrophic mix-up handed the Gorgie men their second.
Adam Jackson failed to find Greg Docherty with a simple 10-yard free-kick and Hearts pounced.
Lewis Moore drove in from the right before cutting back for Bozanic, who gave Boyce a shout to leave the ball before sweeping a stunning finish into the top corner.
And the Hibs fans were flooding for the exits with 10 minutes left when Washington beat the offside trap to catch Hickey's ball over the top before drilling home number three.
Substitute Hallberg's scrambled 89th-minute strike with his first touch after a Daryl Horgan effort was blocked on the line by Dikamona was scant consolation for the hosts.