Mekki not only opened the scoring for the home side just before the half-hour mark but also opened his Shots account as his strike deflected off Shrimpers defender Peter Gilbert.
Fellow midfielder Payne, signed on loan from Oxford until the rest of the season, sealed the 2-0 triumph from the penalty spot in the 64th minute after he was hauled down by goalkeeper Glenn Morris.
A cagey first half was brought to life in the 26th minute when Mekki burst past Gilbert before unleashing a shot which deflected wickedly off the left-back and looped over the rooted Morris.
Danny Hylton could have doubled the lead a minute later but toe-poked wide before Morris spilled an Anthony Straker free-kick just before the break but luckily saw it scrambled away to safety.
However, there was to be no let up for Southend as they dropped from first to third after Payne was brought down by a rash challenge from Morris and slotted home the resulting spot-kick.