There were humdrum periods in this encounter, but they tended to be punctuated by goals. The Ibrox side have now scored 18 times in four league matches, conceding only once, and the superiority of their resources is, for now, being reflected in results.
All eight of the players who agreed to sign as free agents this summer will be available for Rangers' next game, now that the registration embargo has ended. The struggles of last season should be consigned to history, and the home side did not leave any room for anxieties to settle at Ibrox yesterday.
Only 30 seconds had passed when the ball spun off the head of an East Fife defender into the path of Nicky Clark, whose first touch as a Rangers player was to control it and whose second was to slide it past Michael Andrews, the East Fife goalkeeper.
Clark agreed to sign for Rangers 13 weeks ago, and the time spent waiting to make his debut may have focused his intent. "The wee fella showed terrific pace and awareness to finish," said manager Ally McCoist. "He's shown enough in training to indicate that he'll score goals. He plays off the shoulder, runs through, is extremely quick and has a range of finishes."
East Fife began with five players strung across the back, but changed their shape when it became clear that would not be enough to contain the home side.
They occasionally troubled a Rangers defence that was guilty of sitting too deep, much to McCoist's fury.
Liam Buchanan must have thought a clear opportunity was coming when he scurried in behind a static back four, but Sebastien Faure recovered quickly enough to slide in and clear the ball, when even a hint of recklessness would have resulted in a penalty. "It didn't work," said East Fife manager Willie Aitchison of his team's set-up. "Our football was good enough, but we need to make our mistakes up the park, not in front of our goal."
The only way the visitors could accumulate an advantage was in bookings, with four players collecting yellow cards across the course of the game. They could not compete, particularly on the flanks.
Lee McCulloch scored a hat-trick and all three of his goals were created by the full-backs. Lee Wallace crosses resulted in two back-post headers past Andrews from the Rangers captain and Kyle McAusland, with a deft, curling delivery, set up McCulloch's third after the interval, as he again scored with his head.
"In the dressing room he was telling me that was his first hat-trick for Rangers," McCoist said. "I was surprised. It was a brilliant hat-trick, though.
"At his first goal he could have had his head knocked off. The second one, he held the position really well. Then the third he scored from a more central position from a brilliant ball."
Individuals caught the eye, and the most accomplished contribution came from Lewis MacLeod. The midfielder was the beneficiary when a loose clearance bounced in from of him at the edge of the area, but he was bold enough to flick the ball into the air and volley it past the diving Andrews.
As the players celebrated, McCoist mimicked doffing his cap, in recognition of an impressive piece of skill. "Our level of finishing was excellent," the manager said. McCulloch almost added a fourth before the end, rifling a shot from a tight angle just over the crossbar.
The manager smiled ruefully, but the mood was of contentment, since he now has a stronger squad to select from.
Afterwards, he was even meeting chief executive Craig Mather about making one more potential signing, as well as agreeing to possible exits.
"I feel we've started reasonably well," McCoist said, "but that's all it is, a good start."