For all Andy Murray's protestations that missing the French Open through injury was a difficult pill to swallow, it seems his enforced absence could yet pay handsome dividends.

Yesterday, the world No.2 put in a double shift and, in difficult conditions, produced two performances in which he looked sharp, hungry and every inch the favourite to win the Aegon Championship for a third time. With spots of rain still on the wind, he completed a 6-3, 7-6 victory over the Frenchman Nicolas Mahut in a match held over from the previous night and then, with the sun finally out, he crushed Australia's Marinko Matosevic 6-2, 6-2 to progress to the quarter-finals.

"It was good," said Murray, who now plays Benjamin Becker of Germany. "The first match, I thought, was a pretty high standard of grass-court tennis. [Mahut] volleyed extremely well, with some great pick-ups and I just managed to come up with some good passing shots at the right time in the tiebreak."

Resuming at 2-2, Murray saved a couple of break points at 3-4 and then, from 4-3 down in the tiebreak, won four of the next five points to clinch victory over Mahut, who beat him at the same stage here last year.

"My back felt good, he said. "That was what was most pleasing about yesterday with a lot of stops, starts, having to warm up and cool down and stuff. Everything felt good and I woke up this morning with no real stiffness, which is good."

This week's event is the traditional warm-up for Wimbledon and having reached the final there last summer and won Olympic gold a month later, his transition back to grass has been smoother than usual.

"I've definitely got a bit more confidence on the grass this year than I did going in last year," said the Scot. "I know what I did well and what I need to keep doing if I want to have a chance of winning Wimbledon. If I'd had a bad grass-court season last year it would have been hard to know exactly what to do, but I played well last year, was aggressive, I moved well and I practiced extremely well."

Dan Evans' best run in an ATP event was ended, not surprisingly, by the third seed Juan Martin Del Potro, who gave the Briton a bit of a hammering in a 6-0, 6-3 defeat. After a nervy first set, 23-year-old Evans got himself into the match in the second, but Del Potro was too strong and too consistent as he booked a meeting with Lleyton Hewitt, a 5-7, 6-3, 6-4 winner over American Sam Querrey.

In defeating Guido Pella and then the world No. 38 Jarkko Nieminen to reach the last 16, Evans has proved he has ability beyond his current ranking of 277. His position will rise to around 250 after this week and his next task will be to try to win three matches in qualifying to make the main draw at Wimbledon later this summer.

"This week is a good week," Evans said. "It puts me up the rankings a little, gives me a bit of a benchmark to try and reach and a bit of a platform as well. I was playing especially well in Nottingham and before that in the two weeks leading up to it on the grass, so it wasn't an accident that I won matches here and also at Nottingham. I have been working hard and I'm raring to go."

France's Jo-Wilfried Tsonga moved two steps closer to a meeting with Murray in the semi-finals – the Scot beat him in the final two years ago – with back-to-back three-set wins over compatriot Edouard Roger-Vasselin and Igor Sijsling of the Netherlands.

Tsonga will play the unseeded American Denis Kudla in the quarter-finals while the second seed Tomas Berdych takes on the defending champion Marin Cilic of Croatia.

While much of the attention has been on Andy Murray's return from injury, his brother Jamie has quietly been going about his business. Fresh from his win in the Nottingham Challenger last week, the elder Murray brother and his partner John Peers, beat the seventh seeds, Ivan Dodig of Croatia and Brazil's Marcelo Melo, 7-5, 7-6 to reach the quarter-finals.

Murray and Peers have already won one title together – they defeated the world's No.1 pair, Bob and Mike Bryan in the final in Houston in April – and today they have the chance to inflict another upset on the newly-crowned French Open champions.

Colin Fleming and Jonny Marray, seeded fifth this year, kicked off their grass-court season with a 7-6, 3-6, 10-6 win over Benoit Paire and Roger-Vasselin to join Murray and Peers in the last eight.

In the Nottingham Challenger 2, Elena Baltacha, Scotland's former British No.1, continued to remind everyone that she is a handy grass-court player, beating another British player Emily Webley-Smith 6-1, 6-3. Baltacha, who is still making her way back after injury, will play the Czech Barbora Zahlavova Strycova – who was banned for six months until April after testing positive for a banned stimulant – in the quarter-finals.