Aapo Halme's tap-in in the 90th minute rescued a vital point for a Barnsley side struggling at the foot of the table.
However, it was a goalkeeping mistake at the other end that led to the opening goal in the fifth minute when Barnsley keeper Sami Radlinger's poor clearance fell straight to Filip Krovinovic who took two touches and fired over the keeper into an empty net from 25 yards.
Barnsley continued to add pressure in the second half with the best chance before the important goal being a Luke Thomas curling effort from just inside the box forcing another save out of Johnstone.
The hosts had chance after chance and could have won the game, but their final ball was often found wanting.
Struber said: "I feel good and I am very happy with our performance today. I think we were very disciplined and created a lot of chances.
"I think West Brom were, as expected, a difficult team as league leaders, and I think after this game I am very happy with this team.
"We were the better team today with the better chances and the right mentality and character and right match plan.
"The belief in our strength and match plan and we had the right punch and power to change the result. It was a very good game. We are not a relegation team.
"I think the points will come if we have the attitude like this. We have the right mentality to win games.
"A young team we never give up and with this attitude we can beat opponents.
"We have the right quality and also the right character to stay in this league."
West Brom manager Slaven Bilic said: "Of course I am disappointed when you concede late and not get the three points but they did create a lot of chances in the second half.
"It's a big disappointment. We knew it was going to be hard because they've recently got a really good record and are playing good football, especially at home.
"I expected us to be more clinical. We wanted the midfield to be full of good players.
"It is a sticky period, I'm never happy with a point but we have to take it.
"Barnsley are a good team, they run a lot and they came into our box with 4/5/6 players.
"When we conceded we're disappointed but to be fair, they deserved it."