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Second-half goals from Adam Coombes and Dan Walker eased Welling's relegation fears in National League South.
The Wings always had the upper hand against East Thurrock but they took their time before finally taking the three points.
Coombes took his goal tally to 32 for the season and the Wings are now seven points clear of the drop zone.
Welling dominated the first half and should have been a couple of goals to the good by the break.
They had three chances in one minute midway through the first half. Walker's shot was tipped over the bar for a corner, from which Coombes hit the underside of the bar and the ball bounced clear. Then in the resulting move, Harry Crawford made himself space in the box but dragged his shot just wide of the upright.
Coombes also sent a free-kick just wide and then saw his effort from an acute angle cleared off the line by former Dartford man Lee Burns - playing centre-back for the visitors - after neat build-up by Crawford.
Christian Nanetti blazed Welling's first chance of the second half over the bar but Coombes made sure his side went ahead on 66 minutes.
An excellent move involving Crawford and then Walker saw the latter's cross fall to Coombes. His first attempt was parried at the near post but Coombes followed up to slam home.
Crawford, who enjoyed running at the East Thurrock defence, skipped past a couple of challenges before his low shot was beaten away.
The points were made safe with two minutes left when Coombes got in behind the visiting defence. Forced wide by the keeper, he set up Dan Walker who beat the keeper and two defenders on the line to score the second.
Welling: Lewington, Fish, Brown, Hatton, Hayles, Francis, Walker, Waldren, Crawford, Coombes (Slabber 90mins), Nanetti (Williams 90mins). Subs not used: Slabber, Johnson, Leacock, Williams, Fuseini.
East Thurrock: Lidakevicius, Freiter, Osifuwa, Burns, Marvin Ekpiteta, Wood, Gardner (Honesty 75mins), Craddock (Ruel 80mins), Higgins, Heard, Wraight. Subs not used: Walker, Pardoe.
Attendance: 424.