It is the second major upgrade for metals prices since September 2020.
In revising its three-year outlook, S&P noted demand for metals had rebounded but supply remained "stubbornly tight".
"The output for most metals isn't keeping up with resurgent levels of consumption and restocking, which is causing prices to spike early in 2021," it said.
It also recently lifted its forecast for Chinese gross domestic product growth from 7% to 8% and US GDP growth from 4.2% to 6.5%.
Among the metals, copper got the biggest upgrades, with the 2021 price forecast lifted to US$8500 per tonne from $6700/t.
The price is currently sitting at around $8800/t.
"We continue to forecast a strong rise in the demand for copper in 2021 of more than 5% year over year, which will widen the deficit between production and demand above 200,000t," S&P said.
It expects prices to average $8000/t in 2022, up from $6800/t, as supply starts to catch up, and $7500/t in 2023, up from $7000/t.
S&P expects electric vehicles to add at least 1% of additional demand from 2022 onwards, potentially increasing by 2-2.5% under a fast-adoption scenario.
The zinc price forecast for 2021 was increased by $200 to $2600/t, but remains at $2500/t for the following two years.
"We continue to believe that the potential for new supply will translate into relatively limited further upside potential for zinc prices starting next year," S&P said.
Forecasts for aluminium prices were increased by $100 to $1900/t this year and $2000/t for 2022 and 2023.
Nickel price forecasts were left at $15,000/t this year and $14,500/t because of potential new technology developments which could materially expand the resource base for the battery sector.
Iron ore prices for 2021 were increased by $20 to $130/t, and increased from $85/t to $100/t for 2022 and from $70/t to $80/t in 2023.
Forecasts for thermal coal were increased by $10 to $70/t this year, but were left at $60/t for the next two years.
Metallurgical coal price forecasts remain at $130/t this year, increasing to $140/t thereafter.
Finally, S&P left gold price forecasts unchanged at $1700 an ounce in 2021, $1500/oz in 2022 and $1300/oz in 2023.
S&P said the increases would translate to better returns for miners.
"Spot prices are outperforming our higher metal price assumptions in 2021, thus we expect a 15-20% bounce in year-over-year revenue and more than a 20% increase in EBITDA almost across the board for commodity metal producers," it said.
"That said, input costs, as well as local currency costs versus the US dollar, tend to rise with metal prices, which will limit some of their profit gains."