The two sit at 10-under-par 206 through 54 holes of competition. One stroke behind them lies David Kirkpatrick (74) at 9-under, while Heath Slocum (70) and Brenden Pappas (72) are three off the pace.
They day en large belonged to Dodds, who began the round in joint first with both Byrd and Kirkpatrick at 11-under.
Faltering play and early bogies from Byrd and Kirkpatrick, combined with a birdie at No. 8 from Dodds, saw the 41-year-old veteran with a four-shot lead through the first ten holes at minus-12.
It was all to be undone, however, when Byrd turned on the heat late in his round, with birdies at Nos. 12 and 18.
Dodds, on the other hand, recorded a double-bogey at the par-3 17th and a bogey-five at the closing par-4 18th, to drop back into a joint share of the lead.
While Dodds is searching for his first top-10 of the season, Byrd will be vying for his second win of the year on the Buy.Com Tour. He won the Charity Pro-Am at the Cliffs in late April.
With the combination of blustery winds and one of the longest tracks the tour visits all year ' the TPC of Virginia Beach plays to a length of 7,432 yards ' players were met with some of the toughest conditions of the season on Saturday.
Of the 63 golfers who made the cut, only one was able to break 70 in Round Three, when Scott Petersen shot a 69. Fourteen players shot 76 or above, with three of those at 80 or better.
Full-field scores from the Buy.Com Virginia Beach Open