A second-half strike from Michael Woods helped Pools to their first away victory in 14 games.
Pools put in a well-organised and professional display to take all three points from this evening's match at the Cambs Glass Stadium.
Jones's side battled hard for the win, which sees Pools pick up their first points on the road since early October 2016.
Nathan Thomas had the first effort of the game as he stepped up to take a freekick from 25 yards out. The winger decided to go for goal but while his effort had Will Norris backtracking, it found only the roof of the net.
Pools did see plenty of the ball early on and probably just edged the opening fifteen minutes but, as in recent away outings, there was little real threat on goal.
In what was an uneventful first half, Cambridge themselves failed to really test Joe Fryer, though the hosts did have a couple of shots on goal.
Luke Berry turned away from Nicky Featherstone to set his side on the attack, playing it out wide to Harrison Dunk. Dunk showed real pace to race free of Kenton Richardson down the left, earning a nudge in the back for his efforts.
Former Pools loanee Bradley Halliday put a great cross in from the right that found Dunk at the far post. He headed it back into the middle where Berry arrived and smashed it over the bar.
Pools were playing their usual style of passing play and, while Cambridge closed down well, the hosts were more wasteful in possession. But Jones’s men looked organised and determined and, though there weren’t many chances on goal, they contained the U’s well.
Padraig Amond fed it down the line for Lewis Alessandra who was furthest forward for Pools so he went for goal himself with the only shot on goal from open play in the first half – and found Norris waiting to collect his low effort.
Brad Walker, back in the team after missing the game at Notts County on Saturday with an ankle injury, was strong at the back this evening and cleared everything that came his way for a spell mid-way through the half.
Jake Carroll, another familiar face for Pools, sent a lovely freekick in from the left that picked out Gerry McDonagh at the far post but his header went wide of target.
Halliday crossed again from the opposite side, this time picking out Berry but again his effort went wide and the first half finished goalless.
Pools started the second half well, with a fizzing cross from Richardson testing the home defence and only a slight touch from Legge took it away from the waiting Amond.
Nathan Thomas tried his luck with another effort from distance but it went high of target but Pools were at least getting into more of the right areas after the half-time break.
Norris had his best save to make on the hour mark as Padraig Amond caused problems chasing down inside the box, and a panicked header from Scott Wharton had the keeper stretching wide to keep the ball out of his own net.
Cambridge went on to enjoy a strong spell of pressure but Pools were quick to pounce on the break when the chance arrived and snatched the opening goal.
Deverdics, who made a real impression on the game, set the move going, before good work down the right by Alessandra who lifted it into the box for Amond. The striker held off his marker to pick out Michael Woods running into the box and he finished coolly past Norris to make it 1-0.
Joe Fryer had his first save to make shortly after when Max Clark powered a shot in from distance but the on-loan keeper held it comfortably.
Piero Mingoia whipped a deep cross in from the right that was intercepted by Richardson in the air, before Jake Carroll thumped a drive just wide of Fryer’s post.
Scott Harrison headed one off the line as Cambridge upped the pressure, while Carroll tried his luck again, sending another one wide of target.
The hosts had their momentum slowed when Max Clark went in with a strong challenge on Nicky Deverdics down the right wing – the referee reacted quick to pull out his red card as Cambridge were reduced to ten men.
Pools looked to make the most of their man advantage and, when Richardson picked out Amond down the right, the striker played it in for Nathan Thomas who curled an effort at goal, which scraped just wide of the far post.
Cambridge United did have plenty of the ball in the second half but could just not find their way past an organised and determined Pools side, who stuck to their task all evening.
There were some nervy moments in the final minutes of the game but the Pools players put everything in to keep Cambridge out, with bodies in to block shots and chasing everything until the final whistle.
And they got their reward, winning the first game away from home since October, making it a very enjoyable journey home for the 101 travelling Pools fans.
Full Time: Cambridge United 0 Hartlepool United 1
Attendance: 3824 (101 Pools)
Booked: Richardson (32), Woods (60), Alessandra (84), Thomas (85)
Norris, Dunne (Lewis), Legge, Mingoia, Berry, Dunk (Maris), Wharton, McDonagh (Elito 46), Carroll, Clark, Halliday. Cambridge United:
Subs Not Used: Gregory, Taylor, Roberts, Williamson.
Pools: Fryer, Richardson, Harrison, Walker, Donnelly, Featherstone, Woods, Alessandra, Oates (Deverdics 33), Amond, Thomas.
Subs Not Used: Bartlett, Martin, Hawkins, Hawkes, Orrell, Rooney.