Lowry equalled Grégory Bourdy's first round 63 to reach five under par at the Iberdrola Open, moving into second place in the process.
The 24 year old - who burst onto the scene when he captured the Irish Open as an amateur in 2009 - carded six birdies, one bogey and an eagle at the par five sixth.
But England's Wood had extended his overnight lead from three to four with a birdie at the first taking him to nine under after four holes.
Darren Clarke, who shared second place at the halfway stage, was one over through five and sharing third with David Lynn, Thomas Levet and Martin Wiegele.
Course designer and Ryder Cup Captain José Maria Olazábal was enjoying a productive day - the Spaniard was three under through 11 and into a share of seventh place.
Ryder Cup Vice Captain Clarke started with two bogeys in his first three holes, but consecutive birdies at the fifth and sixth saw him join Lowry in a tie for second.
“It was one of those days when it all happened quickly and I was off and running,” said Lowry.
“I was speaking to my coach last night and was saying that we have one of those courses here where you have to stay patient and plot your way round and hopefully the birdies will come. That’s exactly what’s happened over the first two rounds and then today I got off to a great start and was four under through six holes.
“I knew that if I could get into red figures for the tournament then I would have a good chance of a good finish here. I didn’t think I would have a chance to win but you never know now – I just have to wait and see how the leaders get on and see what I have to do tomorrow.”
Wood reached the green in two with a two iron approach at the long tenth and birdied, and produced good par saves at the next two holes to maintain his four shot lead over Clarke, who birdied the 13th to stay in touch.