Following an eighth-placed finish in 2015, Swansea endured a run of just two wins in 17 Premier League games before Francesco Guidolin was named as their new head coach on 18 January.
Salomon Rondon's last-gasp equaliser on Tuesday denied them a win at West Brom.
"We might have [not have] won, but I definitely think we are seeing the old Swansea again," Sigurdsson said.
"We are playing much better than we were. Things weren't good [earlier this season].
"We weren't playing well and keeping the ball like we used to - that's hopefully changing now."
Swansea were in unfamiliar territory after the departure of former boss Garry Monk on 9 December and the playing squad faced criticism.
But after Tuesday's 1-1 draw, Baggies' Welsh boss Tony Pulis believes the Swans have enough quality to avoid relegation from the Premier League this season.
"When in possession, they pass the ball so well and could have scored two or three goals," Pulis said.
"I think Swansea have too much quality to not stay up."
Sigurdsson, the Swans' goal-scorer at the Hawthorns, is currently on his best run of goal-scoring form since his initial loan spell at the Liberty Stadium in 2012, scoring in four of his five appearances so far in 2016.
And the Iceland international felt the Swans had done enough to earn a third straight win on Tuesday.
"It feels a bit like a defeat, to lead coming into the last few minutes," Sigurdsson added.
"We played really well, until the last few minutes. But if you'd have offered us seven points from our last three games, we'd have taken that."
Swansea currently lie in 16th place in the Premier League table ahead of home clashes with Crystal Palace and Southampton.
The "old Swansea City" are back after earning seven points from three games, says midfielder Gylfi Sigurdsson.