Law struck in either half of the Scottish League One clash that saw Arnold Peralta sent off shortly before the interval.
This was the fourth game in 11 days for the Glasgow giants, a fixture schedule that had prompted complaints from boss Ally McCoist.
And his comments led to reports of an alleged foul-mouthed twitter tirade by Stenny striker John Gemmell against McCoist ahead of Rangers' visit.
Gemmell - who has netted 12 goals so far this season - started on the bench, while Rangers were without both Bilel Mohsni and Lewis Macleod for the match at Ochilview.
Mohsni was suspended after picking up a red card following a flashpoint after Thursday's game against Airdrie, while Macleod sustained an injury.
Richard Foster and Andy Little both made their first starts since early November after recovering from their respective injuries.
Rangers had looked unconvincing against the Diamonds, scraping a 1-0 win, and were similarly uninspiring in the opening stages of this encounter.
In fact, the home side would have been ahead after 18 minutes had it not been for the efforts of Cammy Bell.
Sean Higgins pounced on a poor pass-back from Sebastien Faure to take him one on one with the Rangers goalkeeper, who raced off his line and did well to block, before swatting Sean Dickson's rebound shot to safety.
At the other end, a mistake by Nicky Devlin gifted Lee Wallace a decent chance on goal but the left-back was denied the opener by the woodwork as his ferocious strike crashed off the crossbar.
Law succeeded where Wallace failed by leaving the net bulging with 36 minutes on the clock.
A Foster cross was nodded down by Jon Daly into the path of Law who lashed beyond the grasp of goalkeeper Chris Smith.
However, Rangers were dealt a blow four minutes before the break when they were reduced to 10 men after Peralta was dismissed for an ill-timed challenge on Eddie Malone.
The visitors were at a disadvantage in terms of numbers but could have added to their goal tally shortly after the restart.
Little was felled 25 yards out and Wallace stepped up for the resultant free-kick only to drill straight at the goalkeeper.
The controversial Gemmell was thrown into the action on 55 minutes to a smattering of jeers from the away support.
But there was little for either section of the crowd to cheer in a second half that proved to be flat for large spells.
Fraser Aird eventually resorted to a shot from distance that was comfortably claimed by Stenny goalkeeper Smith as Rangers attempted to make their lead a more comfortable one.
Perhaps taking inspiration from the last-gasp draw Stranraer earned at Ibrox recently, Stenhousemuir pushed forward in search of a late leveller.
But clear-cut chances proved hard to come by and it was Rangers who struck again on the 90th minute.
Law drove into the box before rifling a half volley into the roof off the net to wrap up the points.
Then, in the spirit of the holiday season, McCoist grabbed Gemmell for a hug after the full time whistle as Rangers celebrated the win.