The hosts, who gave debuts to a number of players, had the worst possible opening period as Charlton striker Lyle Taylor slotted a penalty after eight minutes, but after a poor first half, Josh Maja's low strike was followed up with Gooch's header as Black Cats boss Jack Ross opened with a win.
The Addicks began brightly on Wearside as new signing Taylor was given an early opportunity to go for goal from a free kick 25 yards out, but the ensuing effort was blazed over the bar.
Karlan Ahearne-Grant was next to have a go from a set piece on seven minutes, but the delivery bounced off the Sunderland wall and went out for a corner which came to nothing.
However, Charlton's early pressure reaped dividends when Chris Maguire brought Grant down in the box in the eighth minute, prompting the referee to award a penalty.
Taylor stepped up and duly slotted a cool spot kick into the top right-hand corner of the Black Cats' net to give the visitors an early lead.
Ross's day would then go from bad to worse as Donald Love suffered an ankle injury and had to be replaced after just 26 minutes.
The hosts did well to keep the deficit down to just one goal and, on the stroke of half time, spurned a golden opportunity to draw level when Josh Maja hesitated in front of goal following a miscued Maguire shot that fell to the 19-year-old's feet.
Both sides began brightly in the second half, before Sunderland claimed a well-deserved equaliser after 65 minutes. Adam Matthews's pass was collected by the striker, who span and drilled a low shot past Dillon Phillips's near post.
The hosts had their tails up and 13 minutes later, the Black Cats could have taken the lead when Maguire's brilliant free kick was parried away by Phillips.
Neither side then looked like snatching a winner, but Gooch had the final say when Bryan Oviedo's cross was headed back across goal and into the corner as Sunderland opened their season with a dramatic win.
Sunderland (4-3-3): McLaughlin; Love (Oviedo, 26), Loovens, Ozturk, Matthews; Honeyman, O'Nien (Sinclair, 45) Mumba; Gooch, Maja, Maguire
Charlton Athletic (4-4-2): Phillips; Solly, Bauer, Pearce (Sarr, 90), Page; Lapslie, Aribo, Pratley, Marshall; Ahearne-Grant; Taylor