The Clarets opened the scoring in the 25th minute as Chris Iwelumo latched onto Jay Rodriguez's flick and headed the ball past Scott Loach from 12 yards.
But the Hornets equalised less than a minute later when Don Cowie hit a left-footed shot into the bottom right-hand corner of the net from 12 yards and they forged ahead in the 57th minute when Martin Taylor rose to connect with Jordon Mutch's cross and plant a firm header into the net.
Brian Laws's men levelled the score 20 minutes from the end when Chris Eagles crossed dangerously and second-half substitute Ross Wallace arrived to fire a left-footed shot into the net from six yards.
The home side continued to probe and claimed the winner in the 77th minute when Taylor fouled Rodriguez and Alexander kept his cool to fire home into the top corner from the penalty spot.
Source: PA
