Despite sitting 12th in the top-flight standings, just seven points separate the Hammers from the relegation zone as the fiercely-contested battle for survival continues.
A shock victory over Everton at Goodison Park on Wednesday saw Palace move above West Ham as they reached the 40-point threshold, often seen as the mark to avoid the drop.
Victory over Palace at Upton Park would take Sam Allardyce's team to 40 points and defender Tomkins revealed West Ham are ready to seize their opportunities.
"We definitely still need a win to keep us from getting sucked in," he said. "People say we are already safe but we can't get carried away about that.
"The teams at the bottom have been winning so we can't be complacent. We have to be prepared for teams below us to get maximum points, that's why we need a win to take us to 40 points.
"It's said that is the safety point and we need to get there as soon as we can. So Palace will be a massive game for us."
Upon Tony Pulis' arrival at Crystal Palace, the Croydon-based club had just four points to their name but have witnessed a spirited revival under the Welshman to steer clear of the relegation zone and all but secure their survival.
"They were actually doing worse than us at one stage," Tomkins said. "But they got themselves out of it and it's going to be a tough game for us at the weekend."
There are calls for Pulis to be named Premier League Manager of the Year and Tomkins believes people need to look beyond the obvious choices at the summit.
"People need to recognise the job that Pulis has done," he added.
"It's not always about the top of the league. You look at Brendan Rodgers and he's an obvious candidate, but then look at the players he has got to deal with.
"But look at Tony Pulis. He's done as good a job as Brendan. Massive."