Cullen, on his 50th appearance, put the Town ahead five minutes before the break before substitute Stevenson scored his first goal for the club with nine minutes left to double the Hatters’ advantage.
And despite the home side pulling a goal back with a stoppage time penalty, the Town held on record yet another victory – their fourth on the road this season – to close the gap on the top three.
The Town began showing one change to the side that beat Southend last week with the recalled Miller – fresh from scoring five goals in 10 games on-loan at Dover – making his debut in the place of Alex Lawless.
Hosts Hartlepool had only scored two goals at home in their previous six matches but they came close to taking the lead in the fourth minute when striker Charlie Wyke’s shot from the edge of the box was parried well by Mark Tyler.
Having won at Exeter last week the hosts started on the front foot, with the Town restricted to attacks on the break.
The Hatters back-line held firm in the face of pressure from the hosts and it wasn’t until the 21st minute that the Town created a chance when Luke Wilkinson’s back-post header from an Andy Drury free-kick was blocked, as was Jonathan Smith’s follow-up in the six-yard box.
As the half wore on, the more the game swung from end-to-end in an entertaining passage of play. It was hearts in mouths time for the Town on the half-hour mark when Wyke went down in the penalty area after Wilkinson’s challenge but referee Tierney signalled no penalty.
Tyler then stopped a goal-bound header from Matthew Bates on 33 minutes, but seven minutes later, out of nothing, the Hatters took the lead. Pelly Ruddock Mpaznu picked the ball up on the right and threaded an inch-perfect ball into the feet of Cullen eight yards from goal, and the striker did the rest, coolly slotting the ball past home goalkeeper and captain Scott Flinders.
Behind at the break the hosts began the second half like the first, putting the Town under pressure, and Tyler needed to be on his toes to keep out Ryan Brobbel’s low shot from the edge of the penalty area three minutes after the restart.
The Town weathered the home side’s early rally in the second half and almost doubled their lead twice in the space of five minutes. Firstly Miller’s first-time left-foot shot whistled inches wide of the post before Wilkinson should have made it 2-0 on 62 minutes when he saw his point-blank header from five yards blocked on the line after he was found unmarked from Drury’s accurate right-wing free-kick.
As Hartlepool struggled to call Tyler into serious action the Hatters continued to search for a second goal. Miller saw a shot blocked following fine hold-up play from Cullen on 67 minutes before Cullen then drove a shot from the edge of the box wide moments later.
Goalscorer Cullen made way in the Town’s first change on 71 minutes when Paul Benson was sent-on by John Still, but whilst Hartlepool upped the ante in search of an equaliser they failed to test Tyler at all.
But the Hatters were always looking a threat on the break and they doubled their lead with nine minutes to play when Stevenson grabbed his first goal in Luton colours. Benson was dragged to the floor inside the D and Miller hammered the resultant free-kick at goal. The ball was parried by Flinders but the ball dropped to Stevenson, first to it, and made no mistake to tap home.
The Hatters kept threatening on the break but while Hartlepool pushed forward for a late consolation the hosts failed to call Tyler into any meaningful save as the clock struck 90.
But just when the Town thought they had kept a sixth clean in seven matches, referee Tierney penalised Scott Griffiths for a foul on Pools substitute Brad Walker in the final minute. The subsequent penalty was dispatched well by Neil Austin.
Three further minutes of added time elapsed without concern as the Hatters held on to secure yet another victory to keep themselves on the coat-tails of the top three.
Town: Tyler; Harriman, Griffiths, McNulty, Wilkinson; Doyle, Smith, Drury; Ruddock Mpanzu (sub Stevenson 79), Miller (sub Guttridge 90), Cullen (sub Benson 71). Subs not used: Lacey, Wall, Walker, Justham.
Attendance: 4,225, including a magnificent 525 backing the Hatters.