While the birdies did not fall as frequently as they had in Friday's round of 62, Na still managed three as he moved to nine-under 201 for the tournament.
"I bounced back nicely and kept myself in it," Na told CBS Sports, adding that he had been distracted by a fan at the 11th.
"From fairway in, I am a pretty good player so I think it plays right into my game," Na said of Colonial, a course he considers one of his favourites.
Spieth, meanwhile, continued his impressive putting to shoot 68 and tie with four others at seven under -- Canadian Mackenzie Hughes (65), Taiwan's Pan Cheng-tsung (68) and Americans Jim Furyk (68) and Tony Finau (71).
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Spieth, the local favourite and a former champion, still had trouble with his ball striking, hitting only four fairways.
A shot into the rough led to his only bogey of the day at 17 after he had made three birdies on the front nine, including a 37-foot putt at the seventh.
"My speed control has been really good this week," the Texan told PGA Tour Radio.
Pan, who goes by the initials C.T., had grabbed the lead briefly after Na's double-bogey but slipped back by dropping strokes on 17 and 18.
Finau could have been a stroke closer but let a shot slip away at the last after driving his ball into the water.
Sweden's Jonas Blixt, the second-round leader by a stroke, was never in contention after a bogey at the first. He shot a four-over 74 to drop four strokes off the pace.
World number three Justin Rose, the defending champion, also turned in a 74 to sit on five-over par 215 after 54 holes.
American Charley Hoffman had the low round of the day, a 63 in morning play to sit three back.
(Reporting by Gene Cherry in Raleigh, North Carolina, editing by Ed Osmond/Peter Rutherford)
