The 46-year-old carded a flawless three-under-par 69 on the Carlsbad course to sit joint-eighth, two shots off the pace, in the LPGA Tour event.
Matthew, who was recently presented with a Scottish Golf lifetime achievement award, birdied the second, sixth and 17th holes.
Four players - Brittany Lang (US), Ai Miyazato (Japan), Jodi Ewart Shadoff (England) and Inbee Park (Korea) - share top spot after they posted matching 67s.
Lurking ominously, one behind, is world No 1 Lydia Ko, who birdied five of the first eight holes.
Matthew’s effort was matched by England’s Felicity Johnson while Charley Hull and Holly Clyburn, who is Matthew’s main rival for an Olympic spot this summer, both opened with 72s to sit joint-39th.
Former Scottish Amateur champion Chris Robb has the leaders in his sights heading into the final round of the MENA Tour’s Royal Golf Mohammedia Open by HLO in Morocco.
The Banchory man shot a four-under 68 in his second round to sit fifth on five-under, just two shots behind four leaders.
Robb, who won his national title at Downfield in 2014, was two-over after four before transforming his day with six birdies, including three in a row from the tenth.
Defending champion Paul Doherty (72-71) is lying joint-19th while Grantown-on-Spey’s Duncan Stewart (72-74) sits in a share of 35th.
South African Tyler Hogarty shares top spot with English trio Zane Scotland, Andrew Marshall and Jamie Elson.
The European Senior Tour will return to Italy after a six-year absence with the announcement of the 2016 Italian Senior Open at Golf Club Udine.
Taking place from 21-23 October, the new €350,000 tournament is part of the commitment to European golf made by the successful Italian 2022 Ryder Cup bid.
It will be the penultimate event of the 2016 season, providing the final opportunity to qualify for the season-ending MCB Tour Championship in Mauritius.
The Italian Senior Open will be the first time a Senior Tour event has been played in Italy since the 2010 Sicilian Senior Open.
It is the second new event on the 2016 Senior Tour schedule, joining the Willow Senior Golf Classic which was announced last month.
For the first time in over 40 years, Moray Golf Club has engaged a golf course architect to help develop a blueprint for the future of its celebrated golf courses. The decision to commission an audit of both 18-hole golf courses continues a precedent established at the renowned club of working with golf’s finest designers.
Swan Golf Designs will be the latest name to join a series of eminent golf course architects who have left their mark on the beautiful stretch of links that overlooks the Moray Firth.
The club’s Old Course, for example with its revetted bunkers and undulating fairways, was laid out by Old Tom Morris in 1889. The tighter New Course was fashioned by three times Open Champion Henry Cotton whose preference for precision resulted in a shorter but equally testing route.
“Moray Golf Club has been associated with a number of legendary names in golf course architecture,” explained John Thomson, captain of Moray Golf Club which will host the qualifier for the 2016 Aberdeen Asset Management Scottish Open.
“When the decision was made to create a masterplan that would enhance the already great holes we have at Moray, it was important to continue that precedent. That’s why we called on Swan Golf Designs.”