The on-loan Aston Villa striker netted twice in the first-half before laying on in-form winger Tom Ince to coolly finish 10 minutes after the interval.
By that point Andre Bikey had headed home to hand Boro a lifeline, but Tony Mowbray's side were second best for long periods as they fell to a third consecutive away loss.
Blackpool substitute Elliot Grandin was brought down by Bikey and rounded off the scoring from the penalty spot, despite Delfouneso being on the pitch to claim a hat-trick denied to him by the linesman's flag moments earlier.
Returning to winning ways after a draw and a loss, Blackpool remain second in the table - four points and six places above Boro.
Ian Holloway rang the changes in his well-stocked, fully-fit squad, recalling captain Barry Ferguson as one of six changes.
Mustapha Carayol made a first league start for Middlesbrough, coming in alongside fellow forward Marvin Emnes as Adam Reach and Luke Williams made way.
The home side started on the front foot with Gary Taylor-Fletcher driving speculatively wide before Ince stung the palms of Jason Steele.
It was not long until Delfouneso sprung the Boro defence to collect Taylor-Fletcher's pass and slide beyond the Middlesbrough goalkeeper.
Grant Leadbitter gave Blackpool goalkeeper Matt Gilks his first work of the evening in the 12th minute, but opposite number Steele was far busier as he did well to thwart Taylor-Fletcher and Delfouneso.
Blackpool continued to pepper Steele's goal as recalled duo Stephen Crainey and Thiago Gomes joined the list of players to test him, but in the 34th minute Boro striker Ishmael Miller wastefully thrashed into the side netting when he had time and space to bag a scarcely merited equaliser.
Two minutes later Delfouneso side side-footed in from Ince's to give the scoreline a more deserving slant.
The 21-year-old passed up a glorious chance for a first-half hat-trick, blazing over after Ferguson and Taylor-Fletcher combined, before a flurry of pressure brought Middlesbrough back into the game as the interval approached.
Josh McEachran's corner was met by Bikey and struck the bar via a clip off defensive colleague George Friend. Blackpool failed to completely clear their lines and, when Leadbitter put the ball back into the box, Bikey made no mistake.
Mowbray's men resumed with similar intent, but the Seasiders restored their two-goal advantage when, played in by Delfouneso, Ince calmly rounded Steele to finish.
Boro enjoyed more of the ball in the second half but, having conceded the third on the counter attack, displayed understandable caution and were rarely able to threaten Gilks.
Delfouneso stooped to head home Grandin's cross-come-shot, only for the celebrations to be cut short by the linesman's flag, before the latter added gloss to the scoreline four minutes from time.