George Kruis and Jack Nowell crossed either side of the interval and Owen Farrell kicked a penalty and a conversion as the Scots, who trailed 7-6 at half-time, were overpowered up front.
Jones picked a starting XV containing 512 caps to begin healing the wounds left by last autumn’s World Cup failure and was rewarded with the result that has offered his regime breathing space ahead of the visit to Rome on Sunday week.
It was a team absent of any debutants and chosen purely to win the Calcutta Cup, but back-row forward Jack Clifford won his first cap off the bench.
Jones has had only two weeks to stamp his mark on England and on the evidence of 80 minutes at Murrayfield, his team has orders to attack from all areas of the pitch and take quick line-outs whenever viable, although the tactics became more conservative – “pragmatic”, in Jones’ words – after the interval.
The execution and decision-making were frequently wayward, however, and familiar failings at the breakdown, in discipline and a lack of cohesion in attack were all too evident.
But there was ruthless precision in the build-up to Nowell’s try, which swept the match out of Scotland’s reach, as forwards patiently punched holes in the defence before the Exeter wing was released into the corner.
Vern Cotter’s men entered the game with the belief they could wrestle back the Calcutta Cup for the first time since 2008 and while they were the more creative, their play was often too frantic.
Jones’ hopes of restoring English set-piece dominance suffered an early blow when a penalty was conceded for a collapsed scrum, but there were clear signs of ambition in the visitors’ early use of possession.
George Ford stabbed an easy drop-goal attempt wide but the assault was quickly renewed and once Billy Vunipola had powered forward from a scrum, Kruis was able to touch down with an outstretched arm while riding a tackle by Jonny Gray.
Scotland were stung into action by the try, guided by the lively Finn Russell who was able to find openings and on one occasion orchestrate a promising attack down the right.
Greig Laidlaw kicked a penalty but missed a routine second as the Scots began to gain a foothold in the game.
The error count from both sides was high but Scotland were making the cleaner line-breaks, with Tommy Seymour threatening off the left wing in a pre-planned scrum move.
An attempt by captain Dylan Hartley to communicate with referee John Lacey resulted in a brief telling-off from the official and England seemed to lose composure as half-time approached.
Russell snatched at a drop-goal when his team would have been better served by continuing to press and the Scots’ ascendency extended into the early stages of the second half, but the scoreboard remained unchanged.
A well-judged kick from Ford gave England the platform to attack and after battering away through Vunipola and James Haskell, they ruthlessly exploited an overlap on the right.
Mako Vunipola offloaded in the tackle to Farrell and the Saracens playmaker neatly sent over a sprinting Nowell.
Farrell was having a mixed afternoon with the boot but when he landed a long-range penalty, England had edged 15-6 ahead.
Laidlaw responded with three points but the Red Rose had a stranglehold on the match and eased over the finishing line.