Leishman was just one shot behind and Smith two off the pace as the quartet of Rahm, DeChambeau, evergreen English star Lee Westwood and surprise Canadian wildcard Richard Lee led the way with their four-under-par rounds of 67 at Sentosa Golf club on Thursday.
Having had to deal with hot and windy conditions on the Serapong Course, the field ended up tightly bunched, with Leishman among a group of seven tied for fifth on three under and Smith in a group of 10 others tied for 12th at two under.
Leishman and Westwood were the only players who managed to go the whole round without dropping a shot.
"There's a lot of trouble out there," Westwood explained, after becoming the oldest player ever to lead a LIV event at the age of 52.
"You don't have to get much out of position for it to become tricky. The rough is not that long, but it is flying rough. You lose a lot of control over the golf ball."
But Rahm has made a fine start in his bid for back-to-back titles after his victory in Hong Kong last weekend. With his five birdies and a bogey in his 67, he recorded a record-breaking 22nd consecutive LIV Golf round under par.
Chile's Joaquin Niemann, who won in Singapore by five shots last year, and Anthony Kim, the emotional winner of the Adelaide tournament, both shot 70s.
The all-Australian Ripper GC were in fifth place in the team event after Lucas Herbert and Elvis Smylie failed to enjoy the best of days, both shooting two-over-par 73s.
Rahm's Legion XIII team, featuring Tyrrell Hatton, Tom McKibbin and Caleb Surratt, were leading that competition on 11 under, 10 clear of Ripper.
