This means the Blues have now taken 14 points from their last seven games and boss Steve Charles is keen for his side, who have three games left, to finish the season on a high.
A blustery wind and rock-hard pitch made the game a largely disappointing affair although Trinity had the better of the chances and deserved their win.
Gainsborough enjoyed the best openings of a dire first half with Richard Pell heading wastefully wide before Ryan Mallon was brilliantly thwarted by Cameron Belford who reacted sharply to scramble away the striker's goal-bound shot from six yards out.
At the other end Trinity keeper Russell Saunders was enjoying a far quieter afternoon, only being called into action to tip over Mark Danks' speculative, curling effort from the left edge of the box.
City should have taken the lead two minutes before the break, however, when Danks whipped in a dangerous cross from the right edge of the penalty area but the unmarked Gary Walker failed to make a connection as he tried to redirect the ball goalwards and the chance was gone.
Worcester rang the changes after the interval in an attempt to break the deadlock, making three substitutions, but it was Trinity who seized the upper hand in the 66th minute when Simon Bird chested the ball down into the path off Needham who coolly slotted the ball past Belford.
City huffed and puffed as they tried to create a decent opening but their afternoon was summed up perfectly when Jamie Price ballooned a promising free-kick high over the bar after City had piled numbers into the box.
Former City favourite Adam Burley almost rubbed his old club's nose in it a minute from time when he was played in by Mallon but saw his low shot blocked by the outstretched leg of Belford.

Worcester City: Belford; Gill (Ricketts 50); Khan; Clarke; Munday; Price; Colley; Walker; Dinsmore (May 59); Craig Wilding; Danks (Burtoft 65).
Trinirty: Saunders, Greenwood, Drury, Parker, Pell, Anson, Austin (Wood 57), Needham, Bird, Mallon, Sleath (Burley 64). SUbs not used: Dudgeon, Reeves, Callery.