Heather Watson and Kyle Edmund both produced battling victories in the first round of the French Open but Naomi Broady was beaten on her Roland Garros debut.
Rain forced the postponement of Watson's match on Sunday night with American Nicole Gibbs, who is Watson's doubles partner this week, a break up early in the third set.
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But Watson won all five games on the resumption to triumph 5-7 6-2 6-2 and set up a second-round clash with former champion Svetlana Kuznetsova.
The result means the British number two has all but secured her place at the Rio Olympics this summer.
Watson, who made that her priority for the season, said: "I actually didn't even think of that at all.
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"I just wanted to win this match, just because I felt I'm hitting the ball really well at the moment, and I would have been really disappointed if I would have lost playing the way I am.
"I slept awfully last night. I couldn't get to sleep. My mind was going over everything in my whole life, not just the tennis match."
The match resumed with Gibbs holding a point for a 3-1 lead in the decider but, once Watson had won that and secured the break of serve, it was largely one-way traffic.
She said: "My first goal was to win that first point, because I knew it was very important. I could have been 3-1 down after just one point.
"I actually had a talk with my coach and we talked for five minutes about how we're going to play that first point. Once I got that, I think I just kind of settled. Especially once that game was done, I started swinging through."
Edmund reached the second round for the second successive year with a 7-6 (7/4) 6-7 (9/7) 7-5 6-1 win over qualifier Nikoloz Basilashvili that lasted two hours and 47 minutes and finished with the darkness closing.
There was not quite the drama of last year, when Andy Murray was among the crowd as Edmund defeated French qualifier Stephane Robert in five sets, but this was another impressive victory, with the 21-year-old Yorkshireman winning nine of the last 10 games.
Georgian Basilashvili is ranked outside the top 100 but came into the match on the back of a title on the second-tier Challenger circuit and three victories in qualifying.
Edmund hurt his ankle in a fall in Nice last week but showed no ill effects, and he said: "It was just a proper match that I felt I did well to come through. It was a real battle out there. My opponent is playing some high-level tennis."
Broady earned her place in a grand slam on ranking for the first time after breaking into the top 100 in February and gave a good account of herself on her least-favourite surface against American Coco Vandeweghe.
Broady was a break up in each set but could not turn that into victory as Vandeweghe triumphed 6-4 3-6 6-3.
Nevertheless, the 30,000 euros in prize money Broady has earned means she can at last wipe out her tennis debts.