Gutierrez set up United’s early goal – scored by Tom Heardman – and played the full 90 minutes.
Kemar Roofe levelled for West Brom in the second half, and Newcastle were indebted to fit-again goalkeeper Jak Alnwick, who pulled off a series of saves to keep the visitors at bay.
Beardsley said: “They played well. Jak made some saves, but without being horrible to Jak, I said ‘that’s your job!’.
“In the last 20 minutes, there was only us that was going to win.
“We got stronger, and obviously once Siem and Gabby had done their time, if you like, we had a couple of fresh legs on.
“It livened us up again. It was a game that could have gone either way, but we’re happy with the draw.”