Molinari and Morrison each had 10 birdies and a bogey in tying the record at the Tanjong Course at the Sentosa Golf Club.
The Singapore Open uses the Serapong and Tanjong courses for the first two rounds. The final two rounds are played on Serapong
Jbe Kruger had a bogey-free 6-under 65 for the low opening round on Serapong. He is tied for fifth with three other players.
Y.E. Yang had six birdies and an eagle in shooting an 8-under 63 and is in third, one stroke behind Molinari and Morrison. Daisuke Maruyama, with nine birdies and two bogeys in the opening round, is fourth at 7-under.
Molinari had a birdie at the second hole and three in a row from Nos. 5-7. His lone bogey came at the ninth hole. He covered the back nine in 6-under 29 with another three-in-a-row birdies on 12-14. Molinari finished his round with a birdie at the 18th.
Morrison had back-to-back birdies on Nos. 2-3 and 6-7 and charged into the lead with four consecutive birdies to open the back nine. He got to 9-under with a birdie at 15 but had a bogey at the 16th hole. He then birdied No. 17 for a share of the lead.
The 62s tied the Tanjong Course record set by Ignacio Garrido last year.