With those two British wins it feels like an excellent time to end this coverage on a high.

We'll be back tomorrow with coverage of Rafael Nadal and Novak Djokovic followed by Aljaz Bedene. You can keep up with the rest of today's matches here.

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British number two Kyle Edmund after reaching the second round: "I controlled a lot of the match. In the third set it showed why in a best of five match you have to keep your concentration. I felt like I was cruising and still went down a break.

"It was good I was able to regain my concentration and finish off in straight sets."

So what next for Kyle Edmund? Possibly a meeting with 12th-seed and home favourite Jo-Wilfried Tsonga.

Tsonga, who regularly goes deep into Slams, has just kicked off his opening match against Argentine Renzo Olivo on Chatrier.

Edmund lies in wait for the winner. If it is Tsonga, and Edmund plays like he did today, then it could be a cracker.

After a disappointing morning, with Johanna Konta's shock defeat, that was a much better afternoon for British fans.

Andy Murray and Kyle Edmund join Aljaz Bedene in round two.

At 0-30, serving for the match, Kyle Edmund could be forgiven for tightening up a little. It doesn't happen. He unleashes two more forehands to get back to 30-30.

Nightmare for Elias. He stops mid-point claiming the ball was long. The umpire disagrees. The point goes to Edmund and that brings up match point...

Kyle Edmund is a game away from the second round. Another fist pump from the British number three as he breaks Elias at the perfect moment. The forehand is fizzing again, just like the early stages of this match.

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Portugal's Gastao Elias puts the pressure on Kyle Edmund, winning a game and making the Briton serve to stay in the set. Will the 22-year-old show any signs of nerves?

There's none evident from young Kyle. Some good serving from Edmund helps him clinch the game.

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Piers Newbery
BBC Sport in Paris

The schedule is out for Wednesday and British number three Aljaz Bedene is last on Court Three against Jiri Vesely, so we're looking at around 17:00 BST at the earliest for that one. Petra Kvitova is first up on Court One against Bethanie-Mattek Sands at 10:00, while Rafael Nadal and Novak Djokovic will be on mid-afternoon duty.

World number one Andy Murray after his first-round win against Andrey Kuznetsov: "He goes for shots, plays very aggressive and tries to take you to the baseline. He has had a good clay court season so I knew it would be difficult.

"Last year was a great year for me and it was the best I have ever played here.

"Every year I have come back and tried to do a a little better.

"I have good memories from Paris last year when I reached the final and I will try to have another good run here this year."

Image source, AFP

Over on Court 14, British number two Kyle Edmund was trailing by a break in this third set but he's got things right back on terms.

A break and two quick service games. Edmo is back at the impressive level of the first couple of sets. What does his Portuguese opponent have left?

A bit more it seems. He holds serve to stop the run of three games in Edmund's favour. Kyle holds as well. We're heading to crunch time in this set.

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Claire Cottingham: That probably wasn't quite as easy as Andy Murray hoped it would

John Arkless: Andy Murray has started to look a little more like himself in the last two sets

So that victory, which came in just over two-and-a-half hours, means Murray will now face Slovakia's Martin Klizan in the next round.

And Klizan's win over France's Laurent Lokoli was an interesting one.

Earlier today, Klizan beat home hope Lokoli in a match that was more notable for the friction between the pair than the tennis.

The Frenchman was not happy with an ecstatic reaction from Klizan to his double fault, accusing him of lacking respect and then refused to shake hands with him at the end of his five-set defeat.

Hope they didn't bump into each other in the locker room...

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We've not seen Andy Murray smiling much today (unless he was being sarcastic during a sticky spot earlier in the match), but finally he breaks out in a grin during his on-court interview with Fabrice Santoro.

Muzza evens lays on the charm, telling the Frenchman he used to love watching him play and that's where his love of drop-shots comes from. Aaah, smooth.

Full quotes to come.

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Ah-ha! The Murray drop-shot has been impeccable today. Another deft backhand spins away from Kuznetsov's reach for 30-30... and that could also be the match.

Wait...Kuznetsov responds with a decent serve that Murray can't bat back with his backhand, but then in the next point the Brit forces deuce...

Image source, AFP

Piers Newbery
BBC Sport in Paris

The sun has finally emerged on day three and a sense of normality has returned over the last couple of sets for Murray. Coaches Delgado and Lendl mutter doubtles insightful tactical titbits to each other, while the rest of the crowd come to life with the end of this one apparently in sight. "Allez On-deeee!" as the locals say.

Kyle Edmund has played at a high level this afternoon but a lull at the start of the third set has cost him his service game.

Perhaps there is life in this match yet. Elias wins the following game as well. Determined stuff from the man from Portugal.

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Barry Flatman
Sunday Times tennis correspondent on BBC Radio 5 live sports extra

It's good that Andy Murray has had two and a half hours on court, that can only be for the good.

When he's put his mind to his tennis he's been easily dominant. I think he's got to cut out the negativity, but will he ever be able to do that?

There will be tougher tests and he will have to play a lot better to get through them.

So here we are. One more game needed for Murray. Can anyone smell a bagel?