James Wilson and Laurent Mendy put the visitors 2-0 ahead at half-time before Hibs rallied early in the second half and pulled a goal back through substitute Adam Mayor.
But the home side's hopes of a fightback were effectively dashed, when Josh McPake - in front of watching Scotland manager Sebastien Pocognoli - scored a superb goal for Hearts shortly after Hibs substitute Jack Iredale was sent off.
It was a seventh successive match unbeaten in all competitions for Hearts, who have recovered impressively after losing each of their first four matches under Vrancken.
The Jambos, agonisingly edged out by Celtic from what would have been their first Scottish title since 1960 on the final day of last season, are now third in the Premiership table with nine points from four games.
Hearts opened the scoring in the 14th minute when McPake got beyond Felix Passlack on the left and cut the ball back for teenager Wilson, who finished well from eight yards out.
Mendy doubled the lead two minutes before the break when he headed in a free-kick from just outside the six-yard box.
Hibernian gave themselves a lifeline when Mayor surged forward and shot high into the net from 15 yards out.
But Iredale, already needlessly booked, then produced a self-inflicted wound for Hibs when he saw red in the 62nd minute after catching Calvin Miller with a high boot.
Hearts made the extra man count within five minutes as McPake seized possession wide on the left and burst away from several Hibs players before letting fly with an angled shot that went in with the aid of a deflection.