Scotland went 31-13 ahead in the 54th minute when Jones’ second try, his team’s fourth, secured a bonus point.
Defeat ended England’s bid for a first Grand Slam in a decade. They are still looking for their first win at Murrayfield since 2020.
England will try to revive their title challenge at home to Ireland a week today.
This was Scotland’s fifth win in six tests against England but their first in eight tests when facing a team in the world’s top 10.
For all their recent success in rugby union’s oldest international fixture, they’ve never finished higher than third in the Six Nations era. They next go to strugglers Wales.
Scotland tore into England, first five-eighths Finn Russell’s fourth-minute penalty breaking the deadlock.
Another Scotland attack ended with Arundell, fresh from his hat-trick of tries in England’s 48-7 rout of Wales at Twickenham, yellow-carded for failing to release after the tackle.
Scotland made their man advantage count when Russell’s clever flicked-on pass released Jones, who rounded England captain Maro Itoje.
Scotland’s speed was proving too much for England’s depleted defence and, after Russell went wide to Steyn on the right, play swept across field with unmarked back-row forward Ritchie scoring a try on the left.
Russell’s third successful goalkick made it 17-0, to the delight of a raucous Murrayfield, with Scotland showing far more in attack than they had during the whole 80 minutes in Rome.
The returning Arundell put England on the scoreboard with a try following a cleverly delayed pass from Ford, whose conversion and 26th-minute penalty reduced Scotland’s lead to seven points.
Scotland had been heavily criticised for squandering a 21-0 lead in a chastening November loss at home to Argentina.
But they reacted to England’s surge with their third try of the half in the 27th minute.
England prop Ellis Genge fumbled Russell’s through kick and halfback White pounced on the loose ball.
Russell again added the extras to make it 24-10.
Ford’s penalty early in the second half cut Scotland’s lead to 11 points.
But Scotland pulled clear again when Ford’s drop-goal attempt was charged down by Matt Fagerson, who released Jones, running clear from halfway for a try between the posts.
Committed defence kept England at bay, with No 8 Ben Earl’s try two minutes from time too little, too late for the visitors.
Earlier, Ireland survived a scare from Italy to win 20-13 in Dublin.
