McGoldrick's magnificent 25-yard strike in the 67th minute led Saints to a first win in seven games and within two points of safety.
Wotte, whose side travel to relegation rivals Nottingham Forest in their final game, said: "The boys showed 100% commitment and are fighting for their lives.
"The players do not deserve to go down and nor do the supporters.
"We are two points from safety with three games to go and we still have Nottingham Forest to play so it is in our own hands. Three wins will keep us up.
"We go to Sheffield Wednesday next weekend and I am not scared of going there because our away form is very good."
The match took a while to spark into life and neither goalkeeper had a save to make until the 22nd minute.
Palace goalkeeper Julian Speroni showed superb reactions to palm away Bradley Wright-Phillips' powerful shot after the striker had cut in from the right.
Wright-Phillips posed a constant threat in a first half dominated by the home side and played a major part in Palace captain Clint Hill being forced to replace the stricken Speroni in goal 10 minutes before the interval.
Speroni came flying across his line to keep out Wright-Phillips' low shot before diving bravely at the feet of Andrew Surman to prevent the Saints midfielder tapping in the rebound.
Surman caught Speroni in the face as he went to shoot and the Argentinian made his way down the touchline with blood pouring from his nose.
With no replacement goalkeeper on the bench, centre-back Hill donned the gloves, reducing the Eagles to 10 men.
Speroni came back for the final minute of the half after being patched up by Palace's medical team, by which time Hill had shown he was an able stand-in by saving well at the feet of McGoldrick.
Wright-Phillips should have scored when he was sent though on Speroni but shot straight into the arms of the dazed goalkeeper.
Speroni continued to take centre stage and produced another brilliant fingertip save to turn Adam Lallana's angled shot behind for a corner in first-half stoppage time.
It was always going to take something special to beat Speroni and it arrived when McGoldrick collected Surman's pass before running at a retreating Palace defence and firing into the top corner.
Palace boss Neil Warnock, said: "We could have been playing all night and not scored.
"We did not have enough quality."