Ben Pope’s header ten minutes from time saw the U’s claim a 2-1 win at ten-man Three Bridges on Saturday.
And the U’s left it even later to win Tuesday night’s home clash with ten-man Sittingbourne.
Jack Dixon fired home Hastings’ winner in second half stoppage time to secure a 2-1 victory and spark pandemonium at the Pilot Field.
The six points sees the U’s up to sixth, just a point off place-above Hythe Town who occupy the final play-off spot.
Wood said: “It shows the character of the team that we have here at Hastings United.
“I’m delighted we got six points in two games. They were two games that we should expect to win, but the circumstances didn’t make it easy.
“A lot of people think playing against ten men should be a lot easier but what happens is, especially when a team has a lead to defend, they can really make it tough for you to break them down. They sit back and waste a lot of time and draw the game out.
“But we didn’t let that bother us. We kept plugging away in both games. They were pretty much identical to each other.
“We didn’t let the gamesmanship affect us and we got our just desserts.
“I’m absolutely delighted we got six points and it sets us up for a tasty affair away at Haywards Heath on Saturday.”
On Saturday, Noel Leighton put Bridges ahead on seven minutes before he was shown a straight red for a high tackle on Tom Chalmers.
Dixon drilled home to level the score on the stroke of half-time. Hastings piled on the pressure and got their reward on 80 minutes when Pope headed home from Dave Martin’s corner.
On Tuesday, Duane Ofori-Acheampong opened the scoring for the Brickies on 22 minutes before Marvin Hamilton-Omole saw red for a wild challenge on Pope.
Chalmers headed home the U’s equaliser on 48 minutes as the hosts bossed the second half. And Dixon popped up at the death to claim a vital three points.
Chairman and CEO Wood was also delighted with the performances of new signing Finn O'Mara, who made his Hastings debut at Three Bridges.
The former Gillingham defender joined the U's on an initial one-month loan deal from Folkestone Invicta last Friday.
Wood added: "He seems to have gelled with the lads pretty quickly and there’s no denying he’s got quality.
"He’s come from Gillingham and played over 100 games for Folkestone Invicta. He’s quality is obviously there and we’re starting to see that.
"He’s strong, winds headers. He’s just a rugged centre half who fits the mould that we are looking for and he’s done well since coming in.
"For him, two wins in two is a great start to his time at Hastings."