The striker, who is the son of Blues manager Paul Sturrock, chested a Josh Simpson cross over Rotherham goalkeeper Andy Warrington and in off the post.
The Millers, who lost on-loan debutant Mark Randall to injury after 22 minutes, replied with Nick Law and Ryan Taylor both having efforts narrowly off target, while at the other end Anthony Grant went close after being released by Michael Timlin.
Southend should have doubled their lead when Sturrock's deflected shot hit the bar and Barry Corr could only scuff the rebound wide, before Nick Fenton and Ryan Taylor both had efforts off target.
The Blues stepped up the pressure in the second half and saw Corr twice head wide before Josh Simpson nodded a powerful effort narrowly off target.
Kevin Ellison headed a tame effort straight at Southend goalkeeper Glenn Morris before Corr rifled a shot just wide with Rotherham keeper Andy Warrington beaten.