The home side enjoyed the better of the first half, with Ricardo Fuller dangerous in attack, but the Royals went closest to breaking the deadlock through Royston Drenthe's free-kick, which was saved by Matt Gilks, and Jem Karacan's 18-yard effort that came back off the crossbar.
Gilks then saved at the feet of Adam Le Fondre in the second period but substitute Barkhuizen stole the show with a run and finish on 75 minutes to seal the points for the hosts.
Blackpool started the afternoon on the front foot and Fuller fashioned the game's first opportunity on 18 minutes, as he tested Alex McCarthy with a left-foot shot from 25 yards.
Reading's central midfield pairing of Karacan and Danny Guthrie were struggling against the Tangerines' dominant midfield trio and Paul Ince's side fashioned their best opportunity of the half midway through the opening period.
After good work from Nathan Delfouneso 25 yards out, Angel Martinez bent a fine cross into the area with the outside of his boot only for the onrushing Neal Bishop to head wide of the top left-hand corner with McCarthy rooted to the spot.
The visitors had been remarkably subdued in the attacking third, particularly given the gung-ho nature of their 3-3 draw with Watford seven days ago, but they rallied at the end of the first half and could easily have gone into the break 1-0 up.
Drenthe found the unmarked Karacan with a free-kick on 43 minutes, but his left-foot volley was cleared away by Gary Mackenzie, before the former Real Madrid man warmed the gloves of Gilks with a curling free-kick from 20 yards.
And with the half-time whistle looming, Karacan struck the crossbar with a delightful lofted effort from the edge of the box after Bobby Grant cleared a corner straight to his feet.
The frenetic end to the first half continued into the start of the second period as Bobby Grant drew a comfortable save out of McCarthy from 25 yards.
Nigel Adkins then brought on Le Fondre for Garath McCleary on 57 minutes and but for the bravery of Gilks, the substitute would have opened the scoring with a close-range effort following Drenthe's mazy run and cross.
There was a sense that a goal was in the offing and on 75 minutes the deadlock was broken at last. Substitute Barkhuizen broke with the ball 20 yards out and after sidestepping two defenders, the 20-year-old fired home to make it 1-0.
And Ince's men saw the game out comfortably in the remaining 15 minutes, with the win taking the Seasiders to the top of the Championship.