Paul Wotton fired the visitors in front from the penalty spot on Tuesday night, before Reuben Reid made sure of a win that boosts Argyle's fight against relegation from League Two.
The visitors could have gone in front in the first half, but Jason Banton's 12-yard shot got a touch from Paris Cowan-Hall who was in an offside position.
The error of judgement did not prove costly as Argyle went ahead in the 57th minute, with Wotton scoring from the spot for the second game in succession.
The penalty was awarded after Bilel Mohsni brought down Joe Bryan inside the area and allowed Wooton to roll a shot into the bottom-right corner of the net.
Shrimpers strikers Britt Assombalonga and Gavin Tomlin were both denied by Argyle keeper Jake Cole, before Reid made sure of the visitors' win with a neat close-range finish in the 75th minute.