Eight points from Marcus Smith and a long-range Fin Smith penalty ultimately settled the contest in the hosts' favour, while there were question marks over the grounding of Tommy Freeman's try, which came between the scores from Scotland pair White and Jones.
Gregor Townsend backed "outstanding goal-kicker" Finn Russell to remain in the role following his trio of costly conversion misses during Scotland's agonising 16-15 Six Nations defeat to England.
Head coach Steve Borthwick, whose side face Italy and Wales next month, said: "I was delighted in the last two games that the endings have gone our way and the team worked exceptionally hard for that.
With a win and a defeat apiece from the opening two rounds of the tournament, the rivals came into a pivotal contest each requiring victory to remain in title contention.
Head coach Townsend insisted he will not be taking the kicking tee from Russell after his side's championship title hopes effectively ended in the wake of the nail-biting finale.
