Wrexham can return to the top of Vanarama National League football with a win at Boreham Wood in Hertfordshire on Tuesday.
The Dragons earned a third successive victory, 3-2 at Havant and Waterlooville, and were the only top seven team to taste success.
Now they are two points behind leaders Solihull Moors with a game in hand.
The trip to Boreham Wood, who are 15th, is a rearranged fixture and the second of three consecutive away matches.
“I want these players to believe that something special could be happening this season,” said manager Bryan Hughes.
“It is about building momentum now. We are just going to look after ourselves. I am not interested in results around us and I said that to the players.
“All I am interested in is what we do. If it is not good enough at the end of the season then it is not good enough.”
Wrexham earned their first National League away win in four months when they returned with three points from Hampshire on Saturday – and immediately targeted two more victories on the road.
The Dragons came from behind to finish 3-2 winners against Havant and Waterlooville in Hampshire, while they now face trips to Boreham Wood on Tuesday and Gateshead next weekend.
Three successive League wins have lifted Wrexham into second place and manager Bryan Hughes said after the success against Havant: “ A good, solid performance and the players showed a lot of character shown to come back from 1-0 down at half-time.
“But we are not as clinical as I would have liked in that final third.
“It was always going to be difficult coming into the game with our current away form. What I’m trying to do is give the lads a bit of belief that we’re a good team and on our day we’re a match for anyone, home or away.
“We need to pick some valuable points up on our travels. There is a big week coming up.”
Former Wrexham striker Joe Quigley put Havant ahead from a first half penalty, but Wrexham hit back with goals from captain Shaun Pearson, Akil Wright and James Jennings.
Alfie Rutherford pulled one back, but Wrexham held on to win and are behind leaders Solihull Moors with a game in hand.
Referee Richard Hulme awarded the home team a penalty after 14 minutes after Wes Fogden seemed to fall into Brad Walker.
It was a controversial decision, but Quigley goalkeeper Rob Lainton the wrong way from the spot-kick to put the Hawks ahead.
Pearson headed in from a corner to equalise after 48 minutes and just before the hour Wrexham were ahead when Wright finished off a flowing three-man passing move down the left.
Two minutes later Jennings took a pass from Tollitt and with just the goalkeeper to beat, drilled his low shot into the far corner.
Jennings ran behind the goal and all the way to the corner flag, high-fiving the Wrexham fans who were delirious as this goal scoring spree unfolding in front of them.
The Hawks hit back after 68 minutes when Alfie Rutherford fired low pass Lainton.
This was also the moment that Oswell was replaced by Chris Holroyd.
Kieran Kennedy made his Wrexham debut, going on for Walker in the last minute.
The away win is a massive boost for the Dragons, who now turn their attention to Boreham Wood away on Tuesday evening.
Havant & Waterlooville: Dudzinski, Williams (Paterson 76), Fogden, Quigley, Robinson, Rose, James (Strugnell 46), A Rutherford, Cordner, Paul, Jalloh (Sekajja 77). Subs not used: Woodford, Harris,
Wrexham: Lainton, Carrington, Pearson, Lawlor, Jennings, Walker (Kennedy 90), Young, Wright, Rutherford, Oswell (Holroyd 71), Tollitt. Subs not used: Dibble (gk), Deverdics, Stockton.
Referee: Richard Hulme (Somerset)
Attendance: 1,658 (250)