The £10million England midfielder's sixth goal in as many games secured all three points - the Black Cats' first in the league in six attempts at the Stadium of Light - and in the process eased them out of the relegation zone for the first time since August.
Johnson struck from close range with 17 minutes gone after Potters keeper Asmir Begovic had spilled Fabio Borini's effort, to the delight of the bulk of a crowd of 34,745.
Stoke's hopes of mounting a fightback were dealt a fatal blow within eight minutes of the restart when midfielder Steven Nzonzi was sent off for a second bookable offence, although Ryan Shawcross looped a header against the bar with six minutes remaining.
Manchester City usurped Arsenal at the top of the table after emphatically ending Tottenham's unbeaten Premier League run under Tim Sherwood with a 5-1 victory at White Hart Lane.
1 Man City 53
2 Arsenal 52
3 Chelsea 50
4 Liverpool 46
5 Tottenham 43
6 Everton 42
7 Man Utd 40
8 Newcastle 37
9 Southampton 32
10 A Villa 27
11 Swansea 24
12 Norwich 24
13 Hull City 23
14 C Palace 23
15 West Brom 22
16 Stoke City 22
17 Sunderland 21
18 West Ham 19
19 Fulham 19
20 Cardiff 18
This was City's 18th win in a 20-match unbeaten run in all competitions, which started with City's 6-0 demolition of Spurs in November.
Spurs were on the end of another embarrassing hiding as Sherwood tasted defeat for the first time in his seven Premier League games at the helm.
Just four minutes were on the clock when Sergio Aguero struck the post - a warning the hosts failed to heed as in the 15th minute he latched onto a David Silva through-ball to direct past Hugo Lloris.
Remarkably, it was the Argentina international's seventh goal in his five appearances since returning from a calf injury and one he looked likely to add to until he limped off late in the first half.
By that point, Spurs were in the ascendancy and thought they had levelled when Michael Dawson turned in a Christian Eriksen free-kick - only for the goal to be chalked off for offside.
Spurs had a further decision to rue moments into the second half, with Danny Rose controversially sent off by referee Andre Marriner for taking down Edin Dzeko in the box.
Yaya Toure slotted home the resulting spot-kick and City extended their lead in the 53rd minute, with Dzeko netting his sixth goal in as many matches against Tottenham.
Sherwood's men attempted to regroup and did pull one back through substitute Etienne Capoue, but City struck again through a replacement of their own, Stevan Jovetic, and captain Vincent Kompany to head into a tough-looking February top of the pile.
Chelsea were frustrated by West Ham in a goalless draw which saw Jose Mourinho's men fall three points behind Man City.
Mourinho on Tuesday played down his side's title chances this term and the Blues saw a seven-game winning run ended by a West Ham side battling relegation and, after leaking goals in recent weeks, defensively resolute.
City, Chelsea's opponents next Monday, scored nine in the two-legged Capital One Cup semi-final with the Hammers, but the Blues faced a defensive wall they could not breach.
Chelsea had won five successive league games and were anticipated to have a comfortable evening against a West Ham side with five points from the previous nine games and deep in the relegation mire.
Yet it was anything but easy as the Blues, who won 3-0 at Upton Park in November, found West Ham to be defensively resilient and organised.
A Villa 4 - 3 West Brom
Sunderland 1 - 0 Stoke City
Chelsea 0 - 0 West Ham
Tottenham 1 - 5 Man City
Christian Benteke's second-half penalty settled a remarkable West Midlands derby as Aston Villa came from 2-0 down to edge a seven-goal thriller 4-3 against West Brom.
A Chris Brunt stunner and a Fabian Delph own goal inside the first nine minutes got the Baggies off to a flyer at Villa Park but the hosts replied quickly through Andreas Weimann, Leandro Bacuna and Delph.
Youssouf Mulumbu made it 3-3 at half-time but Benteke secured only Villa's third Barclays Premier League home win of the season from the spot after the striker himself was fouled.
The result left new West Brom manager Pepe Mel still waiting for his first victory in the job.