Criticism of England's performances had grown in recent months so it felt a big night for the Lionesses and manager Wiegman.
Spain, buoyed by their stoppage-time victory over Belgium on Friday, started off as the stronger of the two sides with Paralluelo causing problems down England's right-hand side.
But Bronze marshalled her well and England's backline, led by captain Leah Williamson, stood solid, forcing Spain deeper as they resorted to shots from outside the box.
Spain boss Montse Tome said after the game she was not surprised by England's defensive performance but felt the result was harsh on her side.
"I think Spain deserved more from the game," she said. "We started the game very well and played at a good tempo. We didn't manage to score and we don't get any points tonight.
"We had chances that we simply didn't take, that's an area we need to improve on and we will improve. England could have scored more too. England scored their goal, we didn't and we just need to keep improving for the next game."
Momentum swung in England's favour midway through the half and they capitalised with James drifting past defenders on one wing, as Park battled and tricked her way through on the other side.
Arsenal striker Alessia Russo, who was on the scoresheet in last week's 1-1 draw with Portugal, impressed yet again and it was her weaving run that led to Park's opener.
"I hope that gives her a lot of confidence," Wiegman said of Park. "I think she grew into the game - she had to adapt and later on she really got into it.
"In possession, we gave Jess the freedom to come inside, a little bit like a number 10. She is very agile. She had to defend too and that is a little different. Sometimes she was really deep and close to Lucy Bronze. It's really nice for the team that we can make different decisions with different players."