Kevin van Veen had equalised for the Iron with 20 minutes to go but, despite having most the pressure late on, it was the referee pointing to the spot that decided the game.
Graham Alexander had made two changes to his Iron side from the 2-0 defeat to Fleetwood at the weekend, as Harry Toffolo and Duane Holmes replaced Conor Townsend and Neal Bishop in the starting 11.
It took Charlton a matter of minutes to produce the game’s first clear sight of goal, after Teixeira volleyed first time following a cross from the right, with the forward only being denied by the frame of the goal.
It took the Iron five minutes to create their first chance, which came courtesy of a short corner, and ended with Jordan Clarke hitting a shot from 30 yards out, which Rudd did well to parry away to safety.
The game then went a little stale for 20 minutes or so, with both sides doing well to cut each other out.
The Iron’s next opportunity would come on 27 minutes as Paddy Madden latched on to Holmes’ deep cross, but the Irishman’s effort only rattled the sidenetting.
Charlton went ahead after the half hour mark as Johnnie Jackson volleyed home Ricky Holmes’ corner.
That would be the last real action of the half, meaning United were trailing at the break at the Valley.
It took 15 minutes in the second period for United to muster up a major opportunity, and it was Clarke again who had the effort. This time it went narrowly wide, as the away side looked to find a way back into the game.
Tom Hopper then made his way onto the pitch and made an immediate impact, as he raced through on goal and forced Jackson into a superb last ditch challenge.
Then, Hopper was again at the front of all things fruitful for the Iron, as Bishop played him down the line and the forward crossed low for Madden to produce a diving header, only for Rudd to pull off a world class save.
United continued to pile forward, and were rewarded for their tenacity with 15 minutes to go, as Hopper’s ball caused havoc in the Charlton box, and Kevin van Veen was there to round the keeper and slot home the equaliser.
A minute after the goal, neat work from van Veen saw him tee up Clarke, but his cross narrowly evaded Madden at the far post.
The visitors were awarded a penalty for a tug as the game entered the 90th minute, and substitute Tony Watt stepped up to hammer it past Daniels.
There was time for one more Iron attack, but Toffolo’s free kick was narrowly headed wide by Matt Crooks.
That would be the final opportunity of a half dominated by the visitors, but cruelly ended by Watt’s penalty.
Charlton Athletic: Rudd, Chicksen, Jackson, Magennis (Crofts, 58), R.Holmes (Ahearne-Grant, 84), Konsa, Ulvestad, Byrne, Novak (Watt, 80), Aribo, Texeira.
Substitutes not used: Phillips, Page, Dijksteel, Dasilva.
Scunthorpe United: Daniels, Wallace, Mirfin (Davies, 90), Dawson, Madden, van Veen, Morris (Bishop, 46), Toffolo, D.Holmes (Hopper, 60), Crooks, Clarke.
Substitutes not used: Anyon, Wiseman, Goode, Toney.
Attendance: 9,088 (301 away).