Playing in the last group out on Friday, Day - who finished joint second in 2011 - carded a 68 to finish six under par, one shot clear of compatriot Marc Leishman and 53-year-old former champion Fred Couples.
And by failing to birdie the 17th or 18th, Day ensured Chinese schoolboy Guan Tianlang - the youngest player in Masters history - made the cut on four-over under the 10-shot rule, despite the 14-year-old earlier being penalised a shot for slow play.
"Wow, that's amazing," Day said when told of Guan's penalty on the 17th, which turned his 74 into a 75 and meant an anxious wait to see if he had made the cut.
"I felt like I played pretty slow out there, but we couldn't go any faster than the guys in front and they weren't too far ahead of us (the group in front containing Tiger Woods took five hours 45 minutes to play their rounds).
"When it means everything to you, you're going to try and do the best you can to play well. And whether that makes you discuss 10 seconds more or 20 seconds more on a shot, you're going to do it, because at the end of the day no one is really going to think about how slow you played if you win the tournament.
"I talked to him (Guan) earlier and he seems a really good kid. It's unfortunate that he received the penalty, but he can learn from that and move on and hopefully play well over the next two days."
The rules state that players will be told when they are out of position on the course, then advised they are being put on the clock and if they subsequently receive two "bad times", are liable to be penalised.