Both teams are struggling in the bottom half of the Premier League table, and went into Saturday's early game at Upton Park desperate for three points.
West Ham had lost four of five league games heading into this encounter, meaning manager Sam Allardyce is under serious pressure.
And West Brom, under the caretaker guidance of Keith Downing as they search for Steve Clarke's successor, were on an eight-match winless run, having drawn their two games under Downing against Hull and Tottenham.
The hosts drew first blood through Joe Cole's fourth-minute opener, but Nicolas Anelka pounced on 40 and 45 minutes to make it 2-1 to Albion at the break.
Sub Modibo Maiga replaced Carlton Cole during the interval, and struck the equaliser on 65 before setting up Nolan's volleyed finish on 67.
Saido Berahino's angled drive on 69 earned a point for the Baggies, though, to ensure the Hammers remain in the relegation zone ahead of two trips to fellow strugglers Fulham and Cardiff.
Nolan was delighted to get on the scoresheet - and urged Hammers fans to stick with Allardyce and his troops despite their lowly standing.
The West Ham skipper told Sky Sports 1: "I'm disappointed. I thought we dominated the first half - and the next thing you know we concede two goals.
"It's what Nicolas (Anelka) does. I played with him for years at Bolton and if you give him chances like that, he puts it in the back of the net - he's got that quality.
"But I thought the gaffer was brilliant at half-time. He told us to calm down and play our way back into the game - and I thought we did that really well.
"You get 3-2 up, the emotions are running high, the crowd are behind you - then you get a bit of brilliance from them, and that's the way it's been going for us for most of the year - we've had a lot of quality goals scored against us."
Nolan added: "We've just got to stick together - it was another fantastic team performance after a good display against Arsenal where we didn't get our just rewards, and I thought we deserved more today, but we've just got to keep going, and I'm sure it'll turn for us."
On his goal, he said: "It was a relief to score and a nice feeling. It's been a bit of a tough season for myself. This is what I've wanted and most of my goals come in and around the box, so I'm delighted with it - but I'm just devastated that it didn't earn the three points.
"Overall we'll take the point and look forward to what's going to be a tough game at Fulham on Wednesday."
The result turned up the heat on Allardyce, whose team have won just three of their 19 top-flight games so far this season.
But Nolan has urged co-chairmen David Gold and David Sullivan to keep the faith, claiming they had been brilliant with the manager, who is having to cope without the services of injured big-money signing Andy Carroll.
He said: "The chairmen have been brilliant with him - they understand what we've gone through this year with injuries and it's just about the club sticking together.
"We've got a great squad here, a great backroom staff, good owners - and we're all in it together.
"We just want the fans to stick with us - and we have no doubt we'll be in the Premier League come the end of the season."