The Canadian faced the worst of the weather, a rain that wouldn't quit, and putted for birdie on all but one hole on Friday, somehow keeping bogeys off his card and had a four-under 68 that gave him a share of the lead with Ben Griffin.
"It was a clean card, which was not necessarily what I expected," Taylor said.
"But it was nice to keep it as simple as possible."
Griffin caught a slight break in the afternoon when the rain relented and Muirfield Village was soft. He had 16 pars, a birdie and a bogey for a 72 that put him at seven-under 137 with Taylor.
Akshay Bhatia (69) is two shots behind, followed by defending champion and world No.1 Scottie Scheffler (70) at four under.
"Really a lot of good ball striking on the front nine to get me a good score there," Scheffler said.
It was the highest 36-hole score to lead the Memorial since 2012. The rain was merely a nuisance that added to what already is a difficult test with rough that players feel will get them prepared for the US Open in two weeks at Oakmont.
"The rough is almost second-to-none, at least for a 'regular' tour event," Taylor said.
"Torrey Pines was pretty thick this year. Bay Hill is always thick. But it seems to be just a little bit thicker here, playing that much more difficult."
Sam Burns played in the tougher morning conditions and shot 65 — 11 strokes better than his opening round — to get within four of the lead. Justin Rose (66) holed out from the fairway on No.3 for eagle and made six birdies on the back nine helping him to even par.
Min Woo Lee (71) and Adam Scott (69) just survived the cut, at three and four over, respectively, but fellow Australian Cam Davis shot a second 78 to finish 12 over.
Japanese star Hideki Matsuyama (75) birdied the 17th and needed par on the 18th to get to the weekend. He hooked his drive so badly on the final hole that it cleared the stream running down the left side of the fairway. From mangled rough, he belted it up toward the green and got up-and-down.
Collin Morikawa (75), who was tied for the lead through six holes, saved par on the 18th from a bunker and was in the group at two-under 142 that included Xander Schauffele (69), who enjoyed four birdies on his last five holes.
With AAP.
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