The British number 10 was also an impressive win for Paul Jub, who saw the 19th seed Thiago Agustin Tirante 6-3 6-2.
Jub served Tirant five times, as he aims to the fifth appearance in SW19 – and the first time the first round is appropriate.
British number 11 Ryan Peniston is also defeating Fesundo Bagnis of Argentina 6-3–3–1 to set up a meeting with Martin Landlus of Spain.
In addition, Hamish is Stewart, who rescued a match point before Monaco’s rival Valentine Veccrot, who retired with injury.
Stewart lagged behind 6-4 6-5 when Vatorrot ended the match early.
Oliver Bonding was the fifth and final British man to win on Monday, who was battling Victor Durasovic 7-5 2-6 6-4 of Norway.
Jan Chinski, who had reached the main draw in each of the last two years, lost 3-6 6-4 6-3 to Mark Lazal of Estonia.
Giles Hussey went down to three sets in Denmark’s August Holmagrain, while James Story fell from 6–0 6–2 to Fifth seeded Tomas Barios Vera of Chile.
The compatriot Alastair Gray was also beaten 5-7 6-3 6-4 by Arthur Bauwier of France.