The Hornets finished sixth in the Championship table to narrowly claim the last play-off berth - they ended level on points with Wolves but, crucially, one goal ahead of the Midlands club on goal difference.
Smith's spectacular goal proved crucial as Watford arrived at Bloomfield Road showing the kind of form which has seen them win just once in their last 13 games.
They started slowly and Burgess goal, on two minutes, left them with a difficult task.
The tall forward claimed his 10th goal of the season when the visitors failed to clear a corner, smashing home the loose ball from six yards with a right foot volley.
Henderson then earned his first yellow card for unsporting behaviour soon after to make matters worse.
Yet Watford rallied and, in the 11th minute, Blackpool goalkeeper Paul Rachubka was forced into a brilliant stop from Nathan Ellington's close-range shot.
Blackpool's on-loan Tottenham youngster Joe Martin rose high to head the ball straight at Watford keeper Richard Lee when he should have done better.
Rachubka - a former Manchester United trainee - excelled himself again moments later with a superb double save, first parrying Smith's left-foot shot from close range before deflecting Henderson's follow-up shot out for a corner.
But Blackpool continued to play the more attractive football after the break and Steve McPhee hammered a vicious shot against the post from distance on 58 minutes.
Watford were reduced to 10 men on the hour when Henderson's challenge on Kaspars Gorkss earned him a second yellow card - and left the Blackpool defender needing treatment.
But that only served to stir Watford into action and Smith, assuming attacking responsibilities, went on a mazy run down the right flank and let fly with a low shot which flew past Rachubka.
Reaching a play-off place only by virtue of their superior goal difference on Wolves will have Watford knowing that they must improve quickly if they are to negioate a semi-final and Wembley final for a place in the Premier League.
Blackpool boss Simon Grayson:
"It's a magnificent achievement by this football club to stay in the division.
"We'd worked so hard for 45 games that we didn't want it to disappear in one game today.
"Eventually we got our just rewards as we've stayed in the division and I think we deserve to."
Blackpool:
Rachubka, Barker, Evatt, Gorkss, Coid, Martin (Morrell 75), Southern, Jorgensen, Hoolahan, McPhee (Fox 88), Burgess (Holt 87).
Subs Not Used: Flinders, Jackson.
Goals:
Burgess 2.
Watford:
Lee, Doyley, Shittu, Bromby, Sadler, Smith, Eustace, McAnuff, Williamson (Mariappa 90), Henderson, Ellington.
Subs Not Used: Poom, Priskin, O'Toole, Ainsworth.
Sent Off:
Henderson (60).
Booked:
Henderson.
Goals:
Smith 62.
Att:
9,640
Ref:
Graham Laws (Tyne & Wear)
