The 23-year-old, who had also been Poole’s match-winner at St Albans on Saturday, netted with an assured finish to settle the issue in favour of the hosts after 53 minutes.
Poole’s second win on the trot, which came following a hat-trick of dispiriting defeats, left them four points adrift of the top five with four games remaining.
Their gruelling end to the season continues with the visits of second-placed Chesham on Thursday (7.45pm) and third-placed Cambridge City on Saturday (3pm).
Poole also host Bashley on Easter Monday before bringing down the curtain on their league campaign against Arlesey Town at Tatnam on April 26.
Boss Killick, who watched his team play their 13th match in the space of 32 days, told the Daily Echo: “I thought we looked reasonably good in the first half but you could tell we were a bit fatigued in the second.
“I just hope our past two results have given us a chance and can invigorate us enough to keep going on Thursday and Saturday, which are two monumental games.
“We just feel we have given ourselves half a chance and I am hoping that will give us something we can use to help overcome the tiredness.
“It wasn’t a great performance and they had quite a young side out but you have to put things in perspective. We have had a number of games in a short space of time and the players have had to put themselves through a lot. I think it is only fair to assess our performance against that backdrop.”
Luke Burbidge, Steve Devlin and Elliott all went close to breaking the deadlock during the early stages as Poole created a flurry of chances, while the crossbar came to the rescue of Hitchin skipper Dan Webb as he almost put through his own net.
Elliott finally found a way past Hitchin goalkeeper Martin Bennett when he seized on the loose ball after Devlin’s corner had only been half cleared, the striker sweeping home his fourth goal of the season.
Killick, discussing a fiercely-contested run-in which will see first, third and fifth travel to sixth, seventh and second, respectively, on Saturday, added: “I am not one of those managers who say we just need to concentrate on ourselves.
“We are in a position where we need other teams to drop points so we can’t just concentrate on ourselves. It is exciting because it looked as if we might be playing out the season in a meaningless way but now we have given ourselves an opportunity to take it right to the end, which is what we always wanted.
“I think it would be difficult for us to do what we want to if we were to lose to Chesham but we couldn’t be in better spirits. Physically, we are tired but, mentally, we go into the game on the back of two very good victories.”
Killick will be sweating on the fitness of Burbidge who was forced off after taking a whack to his foot in the second half. However, Lamin Dibba, Sam Clarke and Michael Charles could be in contention to return to the squad, although the Easter programme is expected to come too soon for Keith Emmerson.
Dolphins: Hutchings, Davis, Martin, Wannell, Whisken, Pettefer, Burbidge (Chiedozie, h-t), Devlin (Davies, 67), Elliott (Gillespie, 79), Preston, Brooks. Unused subs: Lowes, Thomas (g/k).
- Bashley, despite taking a shock first-half lead through Brad Strickland, were eventually beaten 3-1 at Hungerford.