Whyte arrived at Ibrox on Saturday to the applause of hundreds of fans and he would have been happy with what he witnessed from the stand after completing his takeover last night.
Goals from Nikica Jelavic, Kyle Lafferty and Steven Davis, and a Ryan Stevenson own goal, secured a convincing win - as Eggert Jonsson was dismissed - and piled the pressure on Celtic ahead of their game tomorrow.
Walter Smith named an unchanged side from last week's 5-0 win at Motherwell and Lee McCulloch was named on the bench after recovering from knee surgery.
The Jambos drafted David Obua and Ryan McGowan into their team for Marius Zaliukas and Stephen Elliot.
Rangers had a decent chance early on when Sasa Papac picked out Steven Naismith with a lovely 40 yard pass and he slipped into the path of Jelavic but the striker's finish was weak and crept past the post.
Lafferty then claimed for a penalty when he went to ground under pressure from Craig Thomson but referee Iain Brines ignored the appeals.
The best chance so far fell to Hearts when David Templeton whipped across the face of goal for Stevenson and he just failed to connect and stab home at the back post.
Rangers were ahead with 23 minutes gone. Davis provided the cross for Jelavic and he did well to drill under goalkeeper Jamie MacDonald from an awkward angle.
Jelavic then claimed he was tripped in the box by Obua but again no spot kick was forthcoming.
Rangers doubled their lead after 39 minutes when Gregg Wylde's pass found Lafferty and he lashed home from 20 yards.
There was more to come when Wylde again was the provider, this time for Davis to nod home from six yards a minute before the break.
Rangers were hungry for more goals after the break and Jelavic nodded just wide from a corner shortly after the restart.
Hearts were then dealt another blow when they were reduced to 10 men when Jonsson was red-carded for a foul on Jelavic after 62 minutes.
The challenge had sparked a scuffle, which saw Maurice Edu and Naismith both cautioned by the referee.
McCulloch came off the bench to make his first appearance since February and was thrown into the action along with El-Hadji Diouf with 20 minutes to go, as Edu and Jelavic were withdrawn.
The tempo of the match had dipped but Rangers could have had the net bulging when Naismith turned and shot in the box and was only denied a goal of his own by a great save from MacDonald.
But the goalkeeper could not prevent the home side claiming a fourth after 84 minutes. Lafferty's strike was blocked but fell for Diouf whose shot was helped into his own net by Stevenson.
Substitute David Healy then hit the post with a couple of minutes to go with the points already secure.