An intended clearance by Saddlers defender James Chambers rebounded off Eastmond and beat the dive of goalkeeper Richard O’Donnell.
And in failing to get a goal, Walsall, with only two wins in their last 18 games, managed to beat a 60-year-old record by scoring only 21 home goals in a season.
In a low key first half visiting keeper Sam Walker kept out a fierce drive from James Baxendale in the eighth minute, and as Colchester hit back Gavin Massey saw his bending shot saved at full stretch by O’Donnell.
Walsall had the majority of possession but could not make it count. Craig Westcarr spooned one chance high over the crossbar from Adam Chambers’ headed pass before Kieron Morris had a low drive blocked by Walker just before half-time.
The Saddlers pushed forward repeatedly but failed to find a way past the U’s defence, although substitute Amadou Bakayoko had a shot cleared off the line five minutes from the end.