Harry Kane had an early goal incorrectly ruled out but it soon became a tale of frustration for England against the side who famously humiliated them against the odds at Euro 2016.
Kyle Walker's red card teed up the prospect of another ignominious outcome, but Sterling won a spot kick in the final minute when Sverrir Ingason – who, like Walker received a second booking – handled his shot following a right-wing corner.
The Manchester City forward rolled his effort home before a further stoppage-time sting in the tail.
Joe Gomez clumsily fouled substitute Holmbert Fridjonsson in the box, although Birkir Bjarnason opted for a contrasting approach to Sterling's and blazed woefully high and wide.
Kane was flagged offside when he slid in Sterling's sixth-minute cross at the far post. Without VAR in operation, there was no recourse to replays that suggested the goal should have stood.
Walker had a rasping shot deflected into the side netting and, from the resulting corner, Sterling was caught flat-footed and a presentable opportunity went begging – an error that paled next to Declan Rice's horrible air shot from Jadon Sancho's cross.
Set pieces increasingly looked to be England's most potent weapon as their hosts clogged up central areas to rob Southgate's men of any rhythm.
In the 64th minute, Iceland striker Jon Dadi Bodvarsson almost glanced Kieran Trippier's left-wing delivery into his own net.
Frustration was evident when Walker crudely flung himself into a challenge on Arnor Ingvi Traustason to be shown his second yellow card.
Mason Greenwood replaced Kane to win his first cap, meaning England's regular penalty taker was absent when the decisive moment arrived.
Despite his patchy record from the spot at club level, Sterling held his nerve impressively – no guarantee, as Bjarnason handily demonstrated a few moments later.
What does it mean? Iceland's nuisance value here to stay
More than four years since dealing out England's greatest humiliation, Iceland again showed they are no one's fools.
A play-off place for a berth in next year's European Championships demonstrate Erik Hamren's men are no flash in the pan. It would be a brave person who backs against them gutsing their way to the finals once more… unless they are forced into a penalty shoot-out at any stage.
The coolest one
Even considering the shambles of England's 2016, Sterling was at a particularly low ebb. Amid criticism of his performances following an underwhelming first season at City, he dubbed himself "the hated one" on social media.
No one in the England set-up has travelled further and more impressively since then, and a man of considerable stature within and beyond football stepped up as player of his status should do to seal the point.
17 - Raheem Sterling has been directly involved in 17 goals in his last 12 games for England (11 goals, 6 assists). Composed. pic.twitter.com/c5jGYjYPSk— OptaJoe (@OptaJoe) September 5, 2020
Walker's marching orders could leave him with a long way back
Having been shown a yellow card for a 33rd-minute foul on Albert Gudmundsson, a defender of Walker's experience and quality should have known much better when he foolishly erred to be sent off.
The Manchester City man can have no complaints and, with Trippier and Trent Alexander-Arnold already in the mix and Aaron Wan-Bissaka awaiting a first senior cap, he did not need to give Southgate any reason to think ill of him.