The Glasgow club, fresh under the new ownership of David King, were all over their hosts, Lee McCulloch heading over after the wind caught his effort, and Miller firing over the top after a left-wing cross from Lee Wallace.
Miller and Boyd linked up well for Rangers up front throughout the half, but couldn't find an opening as the Blue Brazil, chastened by last week's double-figures loss to Hearts, stood firm.
Rangers almost netted in first-half injury time, but captain Lee McCulloch headed against the post, before nodding another off the bar on the stroke of half time.
Cowdenbeath had the wind behind them in the second half, and took advantage with long balls and efforts from range, although keeper Robbie Thomson had to be alert to save from Nicky Clark's 64th-minute header.
The visitors almost gave it away at the end when Zaliukas back-heeled to a Cowdenbeath player in his own box after a defensive mix-up, but Rangers scrambled clear.
Cowdenbeath's point means that they rise to eighth, above Alloa Athletic and out the relegation playoff zone, while Rangers stay third, three points behind Hibernian.