The Rams dominated the first half at the Riverside, but Frank Lampard’s side were unable to add to the own goal by Boro defender George Friend after 19 minutes despite cutting through the home team’s defence on numerous occasions.
Randolph made a handful of saves to keep the score down, the most eye-catching seeing him push away Harry Wilson’s volley.
With six minutes to go, with Boro having mounted some late pressure, Derby’s Jayden Bogle also scored past his own goalkeeper, volleying into the net when attempting to clear.
It was enough to earn Boro a point that briefly saw them go top of the table.
Pulis said: “In the first half we started really, really poor, really on the back foot. We did some work this week about getting up to the ball but we started really on the back foot.
“We got really sloppy and it just gave them the momentum.
“Randolph kept us in the game and at 1-0 you’ve always got an opportunity and a chance.
“In the second half, the game wasn’t as fluid but we ground it out.
“We worked very, very hard. The lads had a right go and I’ve been involved in games when we’ve played exceptionally well and lost and played exceptionally well and not won a game, so today we haven’t played that well but we’ve ground out a point.”
Middlesbrough: Randolph, Ayala, Flint, Fry, McNair (Braithwaite 51), Clayton, Besic (Saville 55), Friend, Downing, Howson, Assombalonga (Gestede 55). Unused substitutes: Batth, Hugill, McQueen, Lonergan.
Derby County: Carson, Bogle, Keogh, Tomori, Malone, Wilson, Huddlestone, Mount (Johnson 62), Waghorn, Marriott (Nugent 67), Lawrence. Unused substitutes: Forsyth, Jozefzoon, Roos, Holmes, Davies.
Referee: S Hooper (Wiltshire).