Reach gave the Sheffield Wednesday the lead in the 27th minute, but Ghana skipper Andre Ayew cancelled out the lead with a superb finish from Roberts assist in the 60th minute.
Yet a disciplined, hard-working Wednesday display was enough to deny Swansea a fourth successive home victory and give Pulis his first positive result since taking over from Garry Monk on 13 November.
The draw means Swansea stay fourth in the Championship, while Wednesday remain 23rd.
Swansea made so little impact going forward in the first 45 minutes that it felt as if Wednesday had an extra man on the pitch.
The only threats were from the visitors, with Julian Borner firing a shot straight at Swansea keeper Freddie Woodman after a throw-in was not cleared.
Pulis is renowned for his set-piece work, so perhaps it was no surprise that the opening goal of his reign - and Wednesday's first aside from a penalty against Bournemouth in 632 minutes of Championship football - came from a dead ball.
With a crowd of players in the six-yard box, Barry Bannan rolled the ball low towards the penalty spot and the unmarked Reach stroked home first time.
Swansea City: Woodman; Cabango, Bennett, Naughton (Palmer 46); Roberts, Smith, Grimes (C), Bidwell (Manning 61); Dhanda; Cullen (Ayew 46), Lowe (Routledge 61).
Subs not used: Benda, Rushesha, O Cooper, Fulton, Latibeaudiere.
Goal: Ayew 60
Yellow cards: Cabango 26, Grimes 48, Dhanda 57
Sheffield Wednesday: Westwood (Wildsmith 13); Palmer, Lees, Borner, van Aken (Shaw 70); Odubajo, Bannan (C), Luongo (Pelupessy 70), Paterson, Reach; Rhodes (Kachunga 56).
Subs not used: Penney, Dele-Bashiru, Urhoghide, Brown, Hunt.
Goal: Reach 27
Referee: Andy Woolmer