Matthew became the first British golfer to complete an 18-hole round at an Olympic Games on Wednesday as she carded a level par 71.
But just 24 hours later the 46-year-old from North Berwick was climbing up the leaderboard as she opened her second round with three birdies in the opening five holes.
Matthew would add a further three through the back nine, although she did drop a shot at the 14th, to finish with a five-under par 66.
That saw her shoot up the standings and at the end of day two she sits tied for 13th, five shots off leader Inbee Park from South Korea.
With two more days of action to come Matthew is delighted to be in the hunt for an historic Olympic medal.
“I am pleased with how I played and I think I drove it a bit better and gave myself more chances and made some putts,” she said.
“I am five under so I am obviously very pleased and it keeps me in contention which is the main thing. I am edging closer to the lead which is good.
“I drove it better which obviously makes the second shots easier.
“Maybe they were expecting more wind as they were perhaps a little generous on some of the pins but you have still got to play well.
“I’m pleased with where I am and edging closer to the lead and hopefully I can be in there with a chance on Saturday.”
It was a good day for Great Britain at the Olympic Golf Course in Rio with Charley Hull also shooting a five-under par 66.
Hull is eight-under after two days and Matthew is adamant the omens look good as the women look to follow Justin Rose’s lead after he became the first Olympic golf champion for 112 years on Sunday.
“I haven’t played a whole lot with her [Charley] but she hits it pretty long and drives it pretty well,” Matthew added.
“Anyone playing well can shoot a good score here but she is in with a chance too.”
Park, a seven-time major winner, has been struggling with a thumb injury this season but carded a second consecutive 66 for a halfway total of 10 under par and one-shot lead over American Stacy Lewis, who fired 11 birdies, one bogey and a double bogey in a superb 63.
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