Kuchar shot 3-over on the first nine, then rallied with four birdies in a row, from Nos. 12 to 15. The highlight was a chip-in at the 14th hole, and he added another birdie, on a 12-foot putt, at No. 17.
But Kuchar ended on a sour note when he missed the 18th fairway to the right, had to lay up, hit his third shot over the green, then pitched on and two-putted for double bogey.
Before the round started, his father Peter reminded him of a better Saturday 20 years ago, in 1998.
"He was walking to the practice green to the first tee and we remembered that day," Peter Kuchar said. "It's hard to believe."
That day was one of the most memorable performances by an amateur in recent Masters history. With his father carrying the bag, Kuchar was 4-under par through seven holes and finished with a 68. A 72 the next day resulted in a tie for 21st at even-par 288 and Kuchar finished 13 shots ahead of Joel Kribel for low amateur.
Kuchar also earned a return ticket to the 1999 Masters since at the time, the club invited the low-24 players for the next year's tournament.
He said the 20-year span since the 1998 Masters hit him during the first round on Thursday when his group finished late.
"Our group was playing great and walking up [No.] 18, the shadows were long," he said after his round on Friday. "I was really enjoying the day. I thought back to walking up 18 with my dad on the bag and you remember each day going, 'how special is this?' It's amazing how fast time goes. But what great memories I made at this place."
The elder Kuchar said his favorite Masters moment in 1998 came shortly after midnight on Monday, hours after Mark O'Meara won the tournament.
"They invited the low amateur and his family to the champions' dinner and in the whole room, the only people who weren't wearing green jackets were Matt, his mother and I, and [former PGA Tour commissioner] Tim Finchem," Peter Kuchar said. "Then we went to get Matt's stuff out of [the Crow's Nest] and when we came down the stairs we could go right and leave the regular way, or go left and go through the champions locker room."