The goals came within two minutes following an opening spell in which the visitors had looked sharper.
But while Southend did not look anywhere near as dominant as they had done in their last home fixture, when they beat Brentford 4-1, they will have been happy to knock Essex rivals Colchester off the top spot and go two points clear.
Swindon debutant Lee Peacock's tame shot after seven minutes was easily gathered by Blues keeper Darryl Flahavan, before Efe Sodje's header from a Kevin Maher flag-kick was cleared for a corner by Andrew Gurney two minutes later.
The game settled into a scrappy affair with the visitors' five-man midfield nullifying Southend's attempts to get forward.
And it was Swindon who carved out the better chances. Adam Barrett raced in to snatch the ball off the lively Albert Jarrett as he closed in on goal, before the same player's 25-yard looping effort went narrowly over the crossbar.
But the Shrimpers finally warmed the home fans at a freezing cold Roots Hall when Maher lost possession and regained the ball to set up Freddy Eastwood for a shot from the edge of the box that was blocked by Jerel Ifil on 27 minutes.
After signalling their intentions, it took just a further four minutes before the high-flying hosts took the lead.
Gower's cross from the left took a deflection that Town keeper Rhys Evans parried into the path of Mark Bentley at the far post. The midfielder turned the ball back across goal where Guttridge headed home from two yards.
Swindon barely had time to draw breath before they were 2-0 down, after striker Wayne Gray squared to Guttridge, who played the ball into Gower's path for the winger to drill his shot home from 18 yards.
Town manager Iffy Onuora sacrificed Aaron Brown for Jamie Cureton as he started the second half with a 4-4-2 formation, but the visitors nearly found themselves further in arrears within minutes of the restart as Che Wilson and Gray both went close.
Cureton's introduction appeared to have paid dividends on the hour when he capitalised on a Guttridge mistake, but fired agonizingly wide when he should have done better.
Blues should have punished Cureton's wastefulness minutes later when Eastwood turned three defenders and shot just off target. And seconds later Bentley forced a low save out of Evans at his near post.
Four substitutions within three minutes disrupted the flow of the game and the last 20 minutes saw neither side make much headway.
The only chance of the period came a minute from time when Swindon skipper Sean O'Hanlon had a free header from Cureton's corner but saw Flahavan easily save the effort.