Ipswich lost goalkeeper Lewis Price after nine minutes following a foul by Matt Harrold six minutes earlier.
Price continued after lengthy treatment but his hip injury was too much and he was replaced by Shane Supple.
Southend saw winger Simon Francis shoot narrowly over the bar twice, but it was the visitors that enjoyed the bulk of the early possession.
However, it was the hosts that went closest to breaking the deadlock on 19 minutes when Steven Hammell's right-wing cross was cleared by Dan Harding as far as Kevin Maher, who thumped a 20-yard effort inches wide.
Jaime Peters was becoming an increasing threat down the right, so it was no surprise when he set up Town's opening goal. His deep cross found substitute Clarke, who had come on for hamstring injury victim Jon Macken, and the striker placed his free header beyond Darryl Flahavan's dive.
Clarke nearly doubled the advantage with a cheeky looping shot that had Flahavan scampering back before the ball went out for a goal kick.
Southend's heads had dropped after the goal but they finished the half with a flourish after Hammell set up eight-goal top scorer Freddy Eastwood for a one-on-one with Supple, but his shot went agonisingly wide.
Hopes of a Southend revival disappeared two minutes after the restart when Harding's cross was headed clear by Adam Barrett only as far as Legwinski.
The midfielder, who moved to Portman Road in the summer from Fulham, controlled the ball and rifled a shot into the bottom right-hand corner of the goal.
Things got worse for the Shrimpers on 50 minutes when Mark Noble crossed to the right channel where the unmarked Lee fired through Flahavan's legs to claim his fifth goal of the season with the Southend defence nowhere to be seen.
Eastwood and Harrold came off on the hour as both were suffering from a virus. Francis was pushed up front with substitute Billy Paynter and he reduced the deficit on 65 minutes when he latched on to a Luke Guttridge pass and slid a left-foot shot past Supple for his first goal of the season.
The right post came to Ipswich's rescue on 77 minutes when Mark Gower's cross was headed goalward by Clarke, only for his effort to come off the upright and into Supple's arms.
Legwinski was lucky to escape with a yellow card on 82 minutes after lashing out at Francis after the Southend man had caught him with an elbow as the pair jumped for the ball.
Clarke nearly had the last say with a late shot that was collected at the second attempt by Flahavan.