The breakthrough came in the 27th minute of the match, and it was not a surprise that Chris Wood was the player on the scoresheet, with the striker heading a cross from Alex Moreno into the back of the net for his eighth league goal of the season.
Wood then cleared an effort from Lucas Paqueta off the line late in the first period, before West Ham were reduced to 10 men, with Edson Alvarez given his marching orders for diving into a challenge with Anthony Elanga while on a yellow card.
Forest dominated the first half, having 10 attempts to West Ham's one, although there were only two attempts on target from the hosts, with one of those finding the back of the net, as Wood continued his excellent form.
The Reds doubled their advantage in the 65th minute of the match, with Callum Hudson-Odoi's effort from outside the box finding a route into the bottom corner, sparking jubilant celebrations inside the stadium.
Forest were not finished, though, adding a third in the 78th minute through Ola Aina, with the defender finding the back of the net from distance to cap an excellent afternoon for the home side.
Forest have now been victorious in each of their last three Premier League matches, while they are unbeaten since the end of September, with Nuno Espirito Santo's side one of the surprise packages of the season thus far.
West Ham, though, were unable to build on their win over Manchester United last weekend and have now dropped into 14th spot in the table, boasting 11 points from their opening 10 matches of the campaign.
FOREST VS. WEST HAM HIGHLIGHTS
27th min: Forest 1-0 West Ham (Chris Wood)
Forest make the breakthrough in the 27th minute of the match, as Wood heads a cross from Moreno into the back of the net from inside the box; the West Ham defence just could not deal with the in-form striker there.
45th min: Edson Alvarez (red card)
West Ham are reduced to 10 men in the closing stages of the first period, as Alvarez picks up his second yellow card in quick succession for a poor challenge on Elanga; it is a big ask for the Hammers now from this position.
65th min: Forest 2-0 West Ham (Callum Hudson-Odoi)
Forest double their advantage against West Ham, and the goal comes from Hudson-Odoi, with the former Chelsea youngster finding the bottom corner with an effort from outside the box, but the goalkeeper might have done better there.
78th min: Forest 3-0 West Ham (Ola Aina)
Forest have their third at the City Ground and surely secure all three points, as Aina finds the back of the net with a wonderful effort from outside the box; West Ham have simply fallen apart here, but Forest have been excellent again.
MAN OF THE MATCH - CHRIS WOOD
There were a number of impressive performers in a Forest shirt on Saturday afternoon, with Moreno and Hudson-Odoi certainly both worth a mention, but Wood put in a man-of-the-match performance at the City Ground.
Wood scored his eighth league goal of the season in the first half, and he continued to cause West Ham problems, with his presence opening up space for others; the New Zealand international has been one of the best strikers in the league this term.
FOREST VS. WEST HAM MATCH STATS
Possession: Forest 53%-47% West Ham
Shots: Forest 19-4 West Ham
Shots on target: Forest 6-2 West Ham
Corners: Forest 10-5 West Ham
Fouls: Forest 7-9 West Ham
BEST STAT
WHAT NEXT?
Forest will be bidding to make it four Premier League wins in a row when they welcome Newcastle United next Sunday, before heading to the Emirates Stadium to tackle Arsenal in their first match after the November international break.
West Ham, meanwhile, will be aiming to bounce back from the defeat when they welcome Everton to the London Stadium next Saturday, before visiting Newcastle United in their first fixture after the upcoming international break, and Alvarez will be suspended for both of those fixtures after picking up his second sending-off of the season.