Sharma shot a 6-under 66 and Smith followed with a 65 as they finished the second round at The K Club at 13 under for the tournament, one shot ahead of Ross Fisher (66).
Smith, the world No. 85, was the only player in the top eight ranked inside the top 100, with the leading names in the field needing a big weekend to get into contention.
Shane Lowry, who was born about 45 minutes away in Clara, was alone in ninth place after a second straight 68 while McIlroy shot 70 to lie 8 off the lead at 5-under par after a mixed end to his round.
McIlroy, the 2016 champion and No. 2-ranked player, holed out for eagle from 116 yards at No. 16 only to follow that up with a double-bogey at the 17th after finding the rough off the tee and his second shot and missing a bogey putt from 4 feet. He got up-and-down from a greenside bunker for a birdie at the last.
"I thought I played a little better today from tee to green," McIlroy said. "I just didn't hole anything. I hit good putts. I just was misreading them. Some putts lacked a little speed. Some putts I sort of hit through the break. So a little bit of speed control issues rather than anything technical."
McIlroy was tied for 26th place and in a group including Adrian Meronk, the defending champion from Poland who also shot 70.
Sharma, who tied for eighth at The Open at Hoylake on either side of four straight missed cuts on regular European tour events, briefly had a six-shot lead at 14 under after racing to the turn in 28 shots with seven birdies and two pars.
The Indian golfer played the last seven holes in 1 over then saw Smith, an afternoon starter, reel him in.\
"I took a four-week break after The Open and was sick last week so spent most of the weekend sleeping on my couch, but I still have good memories from The Open so I am just trying to continue that form," Sharma said.
The Associated Press and Reuters contributed to this report.