Harrington was joined by fellow Ryder Cup members Miguel Angel Jimenez and David Howell as well as South African Charl Schwartzel in a tie for second.
Groom birdied the opening hole at Hong Kong Golf Club and collected another birdie at the par-4 fourth. Groom then birdied the par-4 sixth to climb to 3 under.
The Australian parred five straight holes around the turn and picked up a birdie at the par-5 12th. Groom then birdied the par-4 13th and tallied his third consecutive birdie at the 14th to take the outright lead.
The 25-year-old parred his way in to maintain a slim advantage over the defending champion.
Harrington, who won this event in dramatic fashion last year, played the back side first and made his first birdie of the day at the par-5 12th. He added a birdie at the par-4 16th to make the turn at minus-2 and continued his fine play on the front side with a birdie at the fourth.
'It's no big deal to be leading after the first day, but you want to be there or thereabouts because you can always play yourself out of the tournament on Thursday,' Harrington said.
The Irishman then birdied the seventh and capped off his round with a birdie at the ninth after his second shot stopped within 10 feet of the hole to finish one behind Groom.
'It's a nice start just to keep the adrenaline and the focus going,' said Harrington. 'The wind was swirling a bit at the end, but I made three of my birdies in the last six holes.'
Jimenez, who was playing in the group ahead of Harrington, birdied the 10th but faltered to a bogey at the very next hole. The Spaniard countered with an eagle at the 12th and collected a trio of birdies on the front nine for his share of second.
Howell had five birdies for a bogey-free round of 65 while Schwartzel mixed seven birdies with two bogeys to join the logjam at 5 under.
Gregory Havret, Derek Fung, Scott Barr, Alessandro Tadini, Bryan Saltus and Harmeet Kahlon share sixth place at 4-under-par 66.