Spaniard Garcia, who is still searching for his first major title, described his first 10 holes - which he completed in five-under par - as "amazing".
Australia's Leishman, who is playing at the Masters for the third time, carded a back nine of 31 to join Garcia on six-under overall and afterwards said he was determined to keep his feet on the ground.
Elsewhere, Tiger Woods began his bid for a fifth title with a "solid" opening round of 70, Rory McIlroy finished on level par after an erratic day and defending champion Bubba Watson recorded his worst score in five appearances at Augusta.
We have compiled all the reaction from the major players after day one of what remains a wide-open tournament at Augusta.
The four-time winner of the Green Jacket admitted he found the Augusta greens tougher than usual after opening his tournament with a "solid" two-under 70.
The Northern Irishman vowed to cut out the careless mistakes after shooting an erratic level-par score of 72.
After a faultless opening day which left him in a share of the lead with Marc Leishman, Garcia was keen to savour the moment.
The Australian was determined to keep his feet on the ground after racing into a share of the first-round lead.
The former World No 1 was delighted with his comeback from a double-bogey at the first hole as he launched his latest bid for an elusive major title.
English debutant Lynn admitted his cautious approach to course management reaped handsome rewards after he carded an opening round of 68.
The popular American rued a bad day on the greens after needing 35 putts as he opened the defence of his Masters crown with his worst score in five appearances.
The Englishman was unable to capitalise on an excellent start to his Masters challenge as he settled for an opening two-under 70 on the first day.
Donaldson celebrated his Masters debut by joining an elite list of players to have recorded a hole in one as he aced the sixth.
The Chinese teenager admitted he felt the nerves at the first tee as he created Masters history by taking over from Matteo Manassero as the youngest player ever to play in the tournament.