David Syers made his first start for Bradford City since injuring his knee in the second match of the season against Leeds United in the League Cup.
With Michael Flynn again out through a stomach virus and Ricky Ravenhill suspended, Syers partnered Ritchie Jones in central midfield.
Jack Compton replaced hamstring victim Kyel Reid on the flank.
City, attacking the Kop, tore into the shrews from the kick-off and whenever the vistiors countered, they found no way past central defender Andrew Davies.
City finally got their reward in the 25th minute when James Hanson nodded home from close range following a corner and strike partner Nahki Wells made it 2-0 five minutes later, the Bermudan outstripping the defence before dinking the ball past onrushing goalkeeper Chris Neal.
City made it 3-0 soon after the interval to put the promotion-chasing visitors firmly in the shade.
Compton cut inside and Neal parried his shot out to Craig Fagan, whose volley went between the goalkeeper’s legs and into the net.
City, however were reduced to 10 men in the 71st minute when Syers received a straight red for what the referee perceived as a reckless challenge on Nicky Wroe 27 yards out - the former Barnsley man soon getting to his feet unscathed.
City were furious when Marvin Morgan bundled the ball in at the far post following a deep cross, claiming the substitute striker had handled as he made it 3-1 in the 78th minute.
For reports and reaction read Sports Monday free inside Monday’s Yorkshire Post newspaper.