On both occasions, Ben Morgan's team needed more than 60 minutes to secure two points, following up a hard-fought 2-1 overtime road win at Basingstoke Bison by beating Bracknell Bees 4-3 on home ice after a shoot-out 24 hours later.
Hull Pirates produced a split weekend, bouncing back from an 8-4 defeat at second-placed Swindon Wildcats with a 5-3 win over Milton Keynes Lighting in East Yorkshire on Sunday.
Leeds Chiefs only had a one-game weekend but it produced their worst performance of the season when they were hammered 9-2 by Peterborough Phantoms.
But it was the Steeldogs who had most to shout about, with Alex Graham the hero in Hampshire when he struck at 62.19 to earn victory after Jan Danecek's seventh-minute opener had been quickly cancelled out by Ryan Sutton's reply for the Bison.
Back on home ice, Morgan's players had to show great resilience to come from behind to earn the extra point against Bracknell.
They had gone ahead through Vladimir Luka's short-handed strike at 9.48, only to be pegged back quickly by William Stead's reply. Graham's power play marker restored the home side's advantage just before the halfway mark, but two goals in 47 seconds - Calum Robertson's strike at 34.19 enhanced by Domink Gabaj's effort - had them on the back foot going into the third.
As the final minute approached, it appeared as if Steeldogs' efforts would go unrewarded, only for captain Lewis Bell to prove the difference maker when he equalised with just 75 seconds left on the clock.
Overtime produced no winning goal at either end, with Luka the hero as the only successful participant in the shoot-out.
After taking an early lead at Swindon through Lee Bonner, Hull Pirates were blasted out the game by the end of the second period which saw them go in 7-1 behind.
Bobby Chamberlain and Sam Towner scored early in the third, but the deficit was too great, Chamberlain grabbing a second at 57.00 before Swindon ensured a four-goal win with a latre strike of their own through Tyler Vankleef.
On Sunday, the Pirates were able to end a three-game winning streak for the Lightning when third period goals from Bonner and player-coach Jason Hewitt proved the difference.
The visitors had gone ahead through Tomas Kana at 17.37 before Bonner struck twice in just under three minutes to put the hosts in the driving seat. That advantage was cancelled out by a power play strike from Kana, only for David Norris to put the hosts ahead again at 35.02 with a power play marker of his own.
But Liam Stewart's strike on the man advantage just over a minute later ensured the teams came out level at the start of the third, Bonner's hat-trick strike proving the game winner with Hewitt's power play strike in the 55th minute providing a welcome cushion.
Leeds' player-coach Sam Zajac admitted he was "embarrassed" and "humiliated" after his side's heavy defeat at Peterborough, although a pointless defeat for eight-placed Raiders IHC ensured they fell no further behind in the playoff picture.
The game was effectively over once Peterborough got themselves 4-0 ahead with just over 12 minutes gone. James Archer got the Chiefs on the board at 15.31 and Radek Meidl added a second just after the halfway mark, but they still went in 6-2 down after 40 minutes, the Phantoms adding insult to injury with three further goals in the third period.
"We were soft, very soft and I hope everyone else was as embarrassed and as humiliated as I felt,” said a frustrated Zajac. “It was the lowest I’d seen the room afterwards, there were a lot of disappointed guys and it was the lowest point for us as a group."