The world number three almost holed his approaches to the last two holes to leave tap-ins for birdie and eagle.
The Northern Irishman carded 70 and trails Andy Sullivan of England.
A fog delay of almost three hours on Friday had seen round two spill into Saturday, when play was again delayed because of mist.
"I needed that," said 26-year-old McIlroy, who is on eight under par.
"I knew 18 was a good chance and 17 was downwind so I would be going in with a wedge, but I didn't quite expect to do what I did on 18. That was nice.
"It glossed over a pretty average round to be fair. But when you are not at your best, to be able to come away with a 70 and keep in touch with the leaders, I'm happy with that."
McIlroy, whose 268-yard five-wood approach to the 18th appeared to graze the edge of the hole, added: "I've never had an albatross and my dad's had one or two so that would have been nice."
American amateur Bryson DeChambeau finished alongside McIlroy after adding a 72 to his opening 64, with world number five Henrik Stenson part of a seven-strong group on seven under.
Rickie Fowler's finish was not quite as spectacular as that of playing partner McIlroy, although the world number six did clatter the flag with his approach to the 16th and also birdied the 18th to finish six under.
In contrast, the final member of the group, world number one Jordan Spieth cut a frustrated figure as he finished with five straight pars to card a 73 and finish three under.

Peter Robinson and Martin McGuinness met David Cameron on Friday.
There is no confirmation on the content of the talks, but it is understood they are likely to have covered financial matters related to the talks process.
NI Secretary Theresa Villiers says she believes a deal is possible next week.
Sinn Féin leader Gerry Adams has predicted that the talks at Stormont will conclude soon.
The round-table talks between Northern Ireland's political parties are aimed at finding a resolution to the crisis at Stormont.
The political row was triggered by a police assessment that IRA members were involved in the murder of former IRA man Kevin McGuigan Sr last month.
Police said the IRA still existed, but added that it was not engaged in terrorism.
Sinn Féin said the IRA has "left the stage".
The talks are also focussing on the issue of welfare reform.
The Northern Ireland parties had agreed on a welfare reform deal in December but Sinn Féin withdrew its support in March.

The Northern Irishman edged ahead of Welsh rival Chaz Davies on the last of the 22 laps to clinch his third successive win in Australia.
Rea's British and Kawasaki team-mate, Englishman Tom Sykes, was third.
"It was a little bit like a bicycle race and no-one wanted to put their nose in front," Rea, 30, said.
The champion's victory - his 39th in WSB - ended Davies' six-race winning streak from 2016.
Rea is one of four riders to clinch back-to-back Superbike titles but is aiming to become the first to win three in a row.
He still lies two titles behind Carl Fogarty's record of four championship successes.
Toomebridge man Eugene Laverty, who is back in the series after two campaigns in the MotoGP paddock, finished eighth on his Milwaukee Aprilia.
There will be a second Superbike race at Phillip Island on Sunday.
Rory McIlroy is two shots off the lead after a spectacular finish to his second round at the Abu Dhabi HSBC Championship on Saturday.
[NEXT_CONCEPT]
The first and deputy first ministers have held a private meeting with the prime minister in London, Downing Street sources have confirmed.
[NEXT_CONCEPT]
Defending world champion Jonathan Rea has won the opening race of the 2017 Superbike World Championship at Phillip Island.