Alfie Mawson headed the hosts in front at the Liberty Stadium, before Shane Long levelled matters after the interval, but it is Sigurdsson who once again proved his worth in Swansea's fight for Premier League survival.
It had been predicted Sigurdsson would be subject to the advances of some of Swansea's top-flight rivals during the January window, but Clement is pleased with his business.
Asked about retaining Sigurdsson, Clement said: "We didn't want to let any of our good players go. Other than that it was to bring in some more quality players.
"We've got [Martin] Olsson, who's working very hard. I'm asking him to do a lot.
"Tom Carroll showed again what a good player he is, and [Luciano] Narsingh has made an impact and created the winning goal.
"Jordan Ayew will join us as soon as he's finished in the Africa Cup of Nations and he'll bring us a lot offensively."
Discussing the victory over Southampton, which followed up a shock 3-2 win at Anfield last time out, Clement added: "A massive result for us, to back up the great away win at Liverpool up with a home win in a really hard game.
"They peppered our box with crosses. We showed big character. Our second goal was fantastic, a great counter.
"The performance was so-so, but the result was massive. We have done more than I expected. Since the heavy loss to Arsenal we have taken one or two really important games."
Clement also confirmed record signing Borja Baston would not be leaving the club, despite reports linking him with a loan move to Villarreal.
"That's not going to be happening. I'm happy he'll be here," he commented.
"[Fernando] Llorente completed 90 minutes today but he's not been doing that regularly.
"I'm more than happy that he's going to be here with us. We need strength in depth. Anything can happen, but we need good players around."
Southampton manager Claude Puel reflected: "We're disappointed of course because it was a game we could do better in. It was a good start in the beginning with a chance through Shane but without being clinical.
"After this, we lost our quality on the pitch without a good control or technical passes and crosses – it was not enough from us."