Playing in his first event since calling an early end to his injury-plagued and winless season in October previous year, four-time major champion McIlroy came into the third round three shots behind Ryder Cup partner Pieters after following up Thursday's 69 with a sparkling 66 on Friday.
"It was another great round and another really good confidence builder", McIlroy said. "Not just for this week but for the rest of the season".
"It would mean a lot".
Vincent sank six birdies yesterday, and on another day, that could have catapulted him somewhere close to the top of the leader-board with a very good chance of causing a major upset at the tournament.
Put another way, he had gone 52 holes since making his last bogey, at the 16th hole of his final round at the Alfred Dunhill Links Championship in October. That's what's nice. I'm back in the tournament and it's something at the start of the year that I wanted to do, contend more. It's felt like a while since I've won and just to give myself these chances; I gave myself a chance at the end of the year [in the British Masters] at Close House and wasn't able to do it. Paul Dunne played too well for me. "When I was back at the Open Championship at Birkdale, just the reception there, playing in front of a home crowd, I knew this is something I just miss". I feel like I've played around with it a little bit, and the results are showing. "I'm excited and looking forward to the challenge".
"My only bogey was from being in a bunker at the 17th, not having a good lie and then finding another bunker".
After the eagle putt, McIlroy yelled, "Finally - one dropped" and punched the air in delight.
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"It was another good day", said Fisher.
From there, he left himself with a 15-foot par putt, knowing he would likely need to make it to get into the final pairing on Sunday.
"I hit a little eight iron into 14, which was probably a nine-iron yardage", McIlroy said.
Pressed about that posture change, he added: "It wasn't much, just moving the ball position a bit, but it certainly made a difference".
The EurAsia Cup team-mates made the most of the ideal scoring conditions on offer at Abu Dhabi Golf Club on Saturday, Fisher shooting a superb seven-under-par 65 to vault into top spot, while overnight leader Pieters made sure he hung on to a share of the lead with a 67. They will partner each other again in the final group for Sunday's final round.
Spain's Jorge Campillo added a 64 to his opening-round 69 to be one behind Pieters, while Alexander Levy of France (65) and England's Ross Fisher (67) were in tied third place at 10-under 134 alongside overnight joint leader Tommy Fleetwood (68), who turned 27 on Friday.
Fitzpatrick carded a nine-under-par 63 to surge into contention on the penultimate day.