Day shot a four-under 68 at Augusta on Friday to stand on six under par for the tournament – one stroke better than veteran Fred Couples and unheralded Australian Marc Leisherman.
Former champion Charl Schwartzel was four off the pace, level with world number one Tiger Woods, after playing a one-under par 71 the second round.
Trevor Immelman, who won the Masters in 2008, was a further shot behind after his round of 75, while four-time Major champion Ernie Els and European Tour Race to Dubai leader Richard Sterne were both on one over, and Tim Clark was a stroke further back.
Schwartzel's round of 71 was a virtual reversal of the 71 he played on Thursday.
In the first round, he was three over after three holes, following a double bogey and a bogey, while on Friday an eagle and a birdie on the second and third holes took him to four under.
He then bogeyed the fourth and seventh to be on two under at the turn. A birdie at the 15th saw him close within two shots of the lead, but another bogey at the 17th left him on a two-under total of 142 for the tournament.
"The course was playing much tougher today," Schwartzel said.
"I think it was playing about four shots harder, so I am happy with my one under.
"Lying just a few shots off the pace with two rounds to play is not a bad place to be."
Immelman was similarly satisfied with his performance.
"I am not too far away and if I play my best golf on the weekend, I should have a chance," Immelman said.
I know what it takes to win here."
South African rookie Branden Grace made the cut at his first attempt, lying on four over after two rounds.
George Coetzee seemed on course to make the cut, but Day's birdie on the 16th brought the cut forward by one, knocking out Coetzee who played a two-over 74 to finish on five over for the tournament.
There was also disappointment for Louis Oosthuizen, who last year lost in a playoff to Bubba Watson. The former Open champion, who carded a 76 to take him to six over for the tournament, missed the cut by two.
"The Masters is a tough tournament and at times you score well and at other times you simply don't," Oosthuizen said.
"I did not do well today, but that is how it goes. I now wish the other South Africans well." – Sapa