It was fitting that Law should score the winner because he was Bradford’s best player as the Bantams were pressed all the way by a Cambridge side fresh from their impressive 4-0 FA Cup over Coventry four days earlier.
His searching runs and intelligent passing were a constant source of danger to Cambridge, but a much-changed Bradford side lacked a cutting edge until Law popped up with the winner in the 64th minute.
Filipe Morais delivered an accurate cross from the right and Law scored a glancing header into the far corner from close range.
Lively winger Mark Marshall had Bradford’s best first-half chance in the 11th minute when he ran on to Haris Vuckic’s pass, but his shot was deflected for a corner.
Cambridge’s Max Clark forced Bradford’s No 2 goalkeeper Rouen Sattelmaier to turn a fiercely-struck shot away for a corner two minutes before the interval.
The Bantams made a bright start to the second half when a neat move begun by Law ended with Jordy Hiwula playing the ball through to Vuckic who shot into the side netting, but Cambridge came close to scoring on the hour mark. Substitute Leon Davies played the ball through for Williamson, but, fortunately for Bradford, Sattelmaier managed to block the shot with his legs.
Law then broke the deadlock and Bradford saw the game out with few alarms.
Bradford City: Sattelmaier, Darby (McMahon 24), McArdle, N Clarke, Kilgallon, Marshall, Dieng (Devine 45), Vuckic (Cullen 63), Law, Morais, Hiwula. Unused substitutes: Doyle (gk), McNulty, King, Hudson.
Cambridge United: Norris, Adams, Dunne, Legge, Mingoia (Ikpeazu 56), Williamson, Dunk, Long (Davies 19), Dallison, Maris (Berry 56), Clark. Unused substitutes: Gregory (gk), Taylor, Roberts, Newton.
Referee: R Lewis (England).