Whelpdale latched on to a deep free-kick from Joe Martin and, with Shrimpers goalkeeper Paul Smith rooted to his goal-line, he cushioned the ball home from close range.
The Gills came close to doubling their lead when a looping effort from Myles Weston was tipped to safety by Smith, who also did well to keep out a 12-yard shot from former United man Adam Barrett.
However, Southend improved in the second half and almost levelled in the 58th minute when a stunning 30-yard shot from Kevan Hurst was impressively tipped over the crossbar by Stuart Nelson.
The visitors had a huge let off a minute later when Barry Corr volleyed wide of an open goal from inside the six-yard box.
But, having weathered the storm, Gillingham almost added a second when Weston fired against the foot of the right post from 12 yards.
