Sigurdsson stepped up to convert his 14th goal of the season as resurgent Reading picked up their ninth win in 11 league games.
Jimmy Kebe had opened the scoring with his seventh goal of that 11-game run but Martyn Waghorn appeared to have earned Nigel Pearson's side a draw with a header before the break.
But the late drama continued Reading's amazing form as the Foxes held on to fourth place in the table to keep dreams of a second consecutive promotion alive.
The Royals had barely broken out of their half after a bright start from the hosts before they took a 16th-minute lead through the transformed Kebe.
Sigurdsson won the ball in the centre-circle and produced an inch-perfect through pass for Kebe to sprint clear.
The Mali international is full of confidence after his recent run of form and showed a deft touch to dance around goalkeeper Chris Weale.
He had gone too wide to finish but was criminally allowed the time to take a touch and steady himself before slotting beyond Weale.
The game opened up and Leicester twice came close to an equaliser through Lloyd Dyer and Andy King before Waghorn did level in the 40th minute.
Dyer was again involved and he took advantage of a slip from Reading right-back Andy Griffin to motor down the wing before picking out Waghorn with a great cross that the on-loan Sunderland man planted in off the base of the far post.
The electric Dyer then picked out King with another superb run and cross but Adam Federici produced a sensational reaction save to tip his effort over the top. Kebe fashioned a chance for Sigurdsson at the start of the second half but King made a goal-saving block on the edge of the six-yard box.
Dyer was then involved in an ugly spat with Griffin and in the aftermath Royals midfielder Jay Tabb had to be carried off on a stretcher with a serious-looking injury after he was clattered by Richie Wellens.
Brynjar Gunnarsson came on in the stricken Tabb's place and it was the visitors who looked most likely to sneak a winner as the half wore on.
Jobi McAnuff and Sigurdsson both saw efforts blocked before Weale made a fine save to keep out a curler from Ryan Bertrand.
Dyer again went close before the Royals stole the win in stoppage time.
Substitute Grzegorz Rasiak found fellow replacement Simon Church with a flick-on and the Wales international cut inside before he went down under a challenge from veteran Nolberto Solano.
Sigurdsson has made a habit of late penalties recently and made no mistake with a cool finish to send the away fans home happy.