Houghton Cricket Club moved further away from the Third Division relegation zone with a hard-fought 2-1 success at Wingate Cons.
However, they had to show character after falling behind to a good goal from the edge of the box in the second minute.
Midway through the first half, Cartner was fouled by the keeper and Greenwood despatched the penalty to make it 1-1.
The second half was an even affair, but Cartner sealed the points for Houghton after a tap-in from a corner.
Incredibly, Houghton are now seventh but still not guaranteed to be safe from the drop.
The Philadelphia rose to second-bottom spot by thumping Hartlepool Vets 8-1, while Rolls-Royce slipped to ninth after a 3-2 defeat to Durham County Strollers.
Ivy Legends consolidated third place with a 7-0 defeat of Heighington Bay Horse.
Pennywell Catholic Club are down to fifth place in the Premier Division after a narrow 3-2 defeat at Hartlepool Workies.
Penshaw fell behind to a penalty, but levelled on the half-hour mark. Workies struck again after the visitors struggled to clear a corner, but the battling Wearsiders hit back to make it 2-2, in off the bar, with the referee adjudging the ball to have crossed the line.
Hartlepool, though, headed a winner five minutes from time.
Workies are level with Marden, who beat Washington Victoria Inn 4-0, but have three games left, to their rivals’ four.
Tony Healer’s header and a Frankie Deverdics brace gave Marden a 3-0 interval lead.
Injury-ravaged Victoria fought valiantly, but star man Steve Hart hit a clincher 10 minutes from time.
Ryhope Foresters, given a walkover against Darlington Shuttle & Loom last weekend, lost 2-1 at Spennymoor Town, but remain fourth.
Redhouse WMC rose to 10th pace with a 2-1 victory over Wallsend Community in midweek.
Third-bottom Hylton CW secured only their fourth win of the season, comprehensively beating bottom club Hartlepool Raby Arms 3-0.
Seaham Marlborough ended their First Division season with a 5-2 home defeat to Whitley Bay Seahorse and a 3-3 draw against Dormans.
They sit in third place but chasers, notably Ferryhill Greyhound, have games in hand.
Sherburn Village beat Consett 2-1 to go seventh, while Grindon Broadway are fifth after a 2-2 draw at South Shields.
Plains Farm Alldec endured heartache with a 3-2 defeat to South Shields Catholic Club in the Ironside Cup final.
Alldec went into the game at Wearmouth CW in great spirits, but the Tynesiders edged home by the odd goal in five to land the Second Division cup.
In Division Two, Alldec lost 3-2 to North Shields Pineapple in midweek, while bottom club Mill View lost 6-3 to the same opposition.
Peterlee Helford rose to third-bottom spot with a 6-3 defeat of Coxhoe Red Lion, after a 2-0 weekend loss to Newcastle East End.
Pennywell Vets cruised to a 9-1 mauling of Pennywell Comrades to climb above their neighbours into eighth place in Division Four.
The Doxy Lad are third-bottom after a 2-0 loss to Forest Hall, while Boldon Colliery Tavern were thumped 6-1 at Hartlepool Tech, who moved above Trimdon Vets on goal difference into second-bottom spot.
Meanwhile, Wearmouth CW Old Boys beat Gateshead Redheugh 3-1 in midweek to clinch their place in next Saturday’s Billy Lorraine Cup final against Sedgefield.