Bolo Zenden's first-half goal was the difference between the sides for much of the second half, but substitute Klasnic headed home on 87 minutes to secure a share of the spoils at the Reebok Stadium.
But Sulley Muntari, on as a second half substitute, went from being zero to hero when his shot from a tight angle was bundled over the line by Knight in the third minute of stoppage time.
Sunderland were the brighter side in the first half, showing signs of real invention in a midfield anchored well by Jack Colback and Jordan Henderson.
However, Bolton had their chances on the break, Daniel Sturridge hitting the bar and the on-loan Chelsea striker almost got to a loose ball from Simon Mignolet's error after a Matt Taylor shot.
But it was Sunderland, with a break of their own, who went in front, and not without controversy. Bolton had appealed for a penalty, claiming that Chung Young Lee had been felled by Steed Malbranque, but the Black Cats poured forward, Stephane Sessegnon releasing Zenden with a perfect through-ball.
The Dutchman sprinted clear of the defence, rounded Jussi Jaaskelainen and slotted home from a tight angle.
Sunderland came out for the second half with the bit between their teeth, with Sessegnon breaching the back four on two occasions, creating a fine chance for Malbranque on 50 minutes, his centre just evading the tricky Belgian.
But Bolton spurned a fine chance to restore parity on 66 minutes when Lee looped a shot over the bar after Phil Bardsley had blocked Sturridge's shot on the line.
Ten minutes from time, substitute Rodrigo fired a 20-yard shot which Mignolet did well to paw away.
Rodrigo had been brought on with Klasnic after 76 minutes, and Klasnic's inclusion meant that Bolton were fielding four strikers on the pitch in a bid to get on level terms. Sunderland, meanwhile, had none.
And, it was such strength in depth that helped Bolton to equalise, when both substitutes combined with three minutes left, Rodrigo's perfect cross from the left found Klasnic at the back post, who headed across goal past Mignolet.
However, Sunderland were not finished, and Muntari received Sessegnon's ball wide left, angled a shot through the tightest of gaps, and wheeled away in celebration when Knight unwittingly gave the travelling Sunderland support much to cheer.
Goals: 0-1 (45+1, Zenden), 1-1 (87, Klasnic) 1-2 (90+3 Knight og)
BOLTON WANDERERS (4-1-3-2): Jaaskelainen; Steinsson, Cahill, Knight, Robinson; Muamba (Gardner 46); Lee (Rodrigo 76), Elmander, Taylor (Klasnic 76); Sturridge, Davies. Subs not used: Bogdan (gk), Petrov, Cohen, Wheater.
SUNDERLAND (4-4-2): Mignolet; Ferdinand, Mensah, Onuoha, Bardsley; Malbranque (Muntari 82), Colback, Henderson, Zenden; Elmohamady, Sessegnon. Subs not used: Carson (gk), Riveros, Knott, Noble, Adams, Lynch.
Referee: Kevin Friend
Attendance: 22,597
Source: Northern Echo
Source: Northern Echo