Pegula got the better of Kudermetova in a come-from-behind triumph as the American posted a 6-7 (9), 6-1, 6-2 victory to move into the subsequent round.
Mandeep Kaur bounced back after losing the opening game to beat Vinot Celine Aurelie of Australia.
The midfielder, capped 109 times for Les Bleues, bows out aged 35.
The title-holders Real Madrid will be expected to remain favourites as the Champions League is back in an all-new format. With Kylian Mbappe as their new star signing, it will
Backing the club bringing in their record-signing in Georginio Rutter, the manager, Fabian Hurzeler expects the move to be a massive success for the club.