The Portuguese manager, who replaced Mark Warburton, got off to a winning start against Hamilton.
American international Emerson Hyndman fired Rangers in front in the 26th minute before Clint Hill tapped home a second four minutes before the break.
Martyn Waghorn earned and expertly put away a 55th-minute penalty before captain Lee Wallace finished off a fine passing sequence to make it 4-0 with 16 minutes remaining.
"I am very happy as we had just four days of work with the players," said Caixinha, who succeeded Mark Warburton.
"If you want to get back a winning culture then the first step is always important."
The result left Rangers eight points behind second-place Aberdeen, whose 2-0 win over Hearts means runaway league leaders Celtic are now unable to clinch the title against Dundee on Sunday.
With Portuguese manager Caixinha urging his players on from the technical area, Rangers looked to get the ball forward as quickly as they could while in possession and pressurise their opponents when they were not.
Their constant pressure paid off midway through the half when Hyndman, on loan from Bournemouth, grabbed the opener.
James Tavernier played a neat one-two with Kenny Miller before cutting the ball back to the American midfielder, who prodded home from close range.
Not content with his equalising strike against Celtic in the Old Firm derby last weekend, veteran defender Hill helped Rangers double their advantage before the break.
On-loan Arsenal midfielder Jon Toral sent a free-kick from out on the right to the far post, where the 38-year-old tapped in from a couple of yards out for his third goal in three games.
Rangers relentlessly pursued a third goal and it came soon after the break when Massimo Donati conceded a penalty for scything down Waghorn from behind.
Waghorn picked himself up to drill his spot-kick straight down the middle to make it five goals in four games against Hamilton this season.
A fabulous passing move resulted in a fourth for Rangers, completing their most handsome win of the campaign.
Waghorn expertly flicked Miller's pass with the back of his heel into the path of the galloping Wallace, who lifted his effort over the head of the advancing Gary Woods and into the net.
Defeat saw Hamilton drop to the bottom of the table on goal difference after Inverness Caledonian Thistle leapfrogged them following a 1-1 derby draw with Ross County.