Meg Mallon posted a 6-under 66 to finish alone in third at 11-under-par 133. She was followed by Juli Inkster, Helen Alfredsson and first-round leader Karen Stupples at 10-under-par 134.
Kane played the back nine first at Corning Country Club and two-putted for birdie at the par-5 12th. She dropped a 9-iron inside four feet for a birdie at the 15th and drained a 20-foot putt at the 18th.
The Canadian continued her fine play on the front half with a birdie at the first and made it two in a row with a birdie at the second.
Kane then birdied the eighth and hit an 8-iron to 20 feet at the ninth. She drained the putt to secure her share of the 36-hole lead.
'It was all pretty good,' said Kane. 'I hit a lot of greens, gave myself some chances, the putter was rolling well. I was quite comfortable.'
Matthew was on fire early with three birdies over her first five holes to reach 7-under. She parred her next six holes before rekindling the spark on the inward half.
Matthew eagled the par-5 12th and followed that up with a birdie at the 13th. She then birdied the 14th and capped her round of 64 with a birdie at the par-4 17th.
'I played really well today. I had a lot of chances, missed a few, so it's probably all evened out now,' said Matthew. 'I've played over here now for nine years. When I go home, I don't really play, because the weather is too bad. Maybe I'm getting soft.'
Stupples, who was disqualified from this event last year for missing her tee time, had a much quieter round than the blistering 64 she fired on Thursday.
She started on the back nine and found trouble early with a bogey at the 13th. Stupples responded with a birdie at the 15th and collected three birdies and one bogey the rest of the way to finish two shots off the lead.
Beth Daniel carded a 66 to finish alone in seventh at 9-under-par 135. Rosie Jones, a two-time champion of this event, was one shot further back at 8-under-par 136.
Jones was joined by Mi Hyun Kim, Soo-Yun Kang, Anna Acker-Macosko, Wendy Ward and Patricia Meunier-Lebouc in a tie for eighth.
Defending champion Laura Diaz posted a 2-under 70 to survive the 36-hole cut. The cut line fell at 1-under-par 143 with 81 players qualifying for the weekend.