Managerless Welfare, with only a point from their opening four matches, threatened to spring a surprise when young Andy Price netted his second goal of the game 12 minutes from time.
But the in-form home side, seeking a fifth straight win, refused to buckle and just three minutes from time substitute Elliott slotted home to deny his old club maximum points.
Collieries were good for a point. In a game of few clear-cut chances, they carried the main attacking threat through the pace of striker Ben Gilbert and should have put the game to bed early in the second half when they carved out some glorious chances without forcing a save from visiting stopper Dane Whittleston.
Ponte' forced the early pace. Centre-half Matt Wilkinson nodded home Gilbert's far-post free-kick, only to be denied by an offside flag, and minutes later ex-Nostell hit-man Gilbert skipped away from his marker to flash a shot wide of the far post.
Welfare survived the early storm to take the lead with a soft goal from Price, who prospered from a blunder from home stopper Chris Darby, and it was almost 2-0 when John Coppinger span his marker to unleash a fierce drive just over the top of Darby's frame.
Burly Glasshoughton centre-half Rudy Coleano showed his class to head a dangerous cross wide at the expense of a corner after great work between Gilbert and Dean Lackie and on 40 minutes Colan Leung thwarted Lackie with a vital tackle that saw the young full-back make an early exit with an ankle injury.
Ponte' levelled with the final act of the first half. A handball on the edge of his own box from Glasshoughton full-back Andy Targett conceded a free-kick in a dangerous position and Gilbert's delivery to the far post was met by Wilkinson, whose well-placed header back across Whittleston found the far corner.
The goal gave the home side a lift for they dominated on the restart. Combative midfielder Dean Helliwell should have hit the target with a close-range header and the same player blazed over from the edge of the box after Welfare's defence struggled to clear.
Gilbert released Lackie with a glorious pass but his low shot was easy for Whittleston and when Lackey's surging run released the beefy Sean Hammond to cross, Gilbert should have done better with a free header.
Glasshoughton weathered the storm, with the hold-up play of Nigel Croad a feature, before a floodlight failure pitched the railway side of the ground into semi-darkness.
Upset
Play resumed after a 20-minute wait but the delay seemed to take the sting out of the game, with clear chances at a premium now.
Price looked to have caused an upset but Elliott, allowed to go on despite strong appeals for offside, had the final word.
Meanwhile, Welfare have had 12 applications for the vacant first-team manager's post. Six will be interviewed by the club's management committee on Monday and Tuesday, with officials hopeful of making an appointment before the trip to Brighouse on September 13.
Director of football Ray Gowan said: "This is a vital appointment after a year of disappointing results for the club who have great ambitions to regain their Premier Division status and ultimately progress beyond this level.
"The rest of the club is in great shape, consistently winning football matches at all levels, from the reserves to the under-10s, and it is vital that the flagship first team, which is still one of the best supported in the league, starts to emulate the success of the rest of the club.
"The new man must be well connected in local football circles and possibly have experience of levels higher than the NCE League. He must be totally focused on results with immediate effect and prepared to bring in new faces but also be aware of the young talent already in the club's reserve and under-19 teams."