The former Stoke City forward has scored nine goals and added four assists in his last 14 games as he looks to help the Hammers stay in the Premier League, most recently setting up Javier Hernandez's equaliser in their morale-boosting 1-1 draw with Chelsea.
And despite the draw edging West Ham closer to safety, Carroll insists no club is safe.
Peter Crouch climbed off the bench to take advantage of a Joe Hart error to put the visitors ahead before Andy Carroll struck late on to snatch victory away from Lambert's men.
West Ham manager David Moyes believes record signing Marko Arnautovic is "a little bit of a Zlatan", as the Austrian enjoys a rich vein of form.
They are six points clear of the relegation zone and face Stoke on Monday night in a game which could see Arnautovic shove his old club a step closer to the Championship.
"The goal was a kick in the teeth", Crouch said. In his first game back, he made a mistake for a goal in a 3-0 loss at Burnley on March 10, and this one against Stoke was nearly an exact replica as he fumbled a shot in front of him by Xherdan Shaqiri.
Although Rice is still very young and is developing, one should not be surprised if he establishes himself in the West Ham first team next season. As usual, he caused havoc after coming on, and his goal is likely to prompt calls for his inclusion in England's World Cup squad as a Plan B for coach Gareth Southgate, fitness permitting.
Things are pretty rosy for West Ham at the moment after their point at Chelsea gave them a bit of breathing space above the bottom three. "We're right in the fight, no mistake about it".