He will now play veteran Fernando Verdasco in the next round, which will provide a much sterner test for the 24-year-old.
Edmund came on to court after women's second seed Naomi Osaka had been dumped out by Yulia Putintseva, but even though he got off to a scratchy start, losing the first two games, there was never much chance of another shock.
Watson kicked off the home charge at this year's tournament by seeing off Caty McNally, a 17-year-old qualifier, in straight sets, winning 7-6 (3) 6-2, as she opened the action on Court 12 at 11am.
She served three double faults in the very first game - including one serve which bounced before the net - and had to save two set points in the opener before eventually taking it on a tie-break.
The second set was a much more routine affair, but even then the 27-year-old, playing at her 10th Wimbledon, said she did not enjoy the match until it was done and dusted.