* South African rand lags on lockdown fears

* Russian rouble benefits from high oil prices

* Turkish lira rises on real money account holding

* EM stocks at 13-year high

Jan 6 (Reuters) - Emerging market stocks and currencies in Europe, the Middle East and Africa rose on Wednesday as the prospect of a Democrat-controlled U.S. Senate pressured the dollar and drove capital flows into riskier assets outside of America.

U.S. stock futures and the dollar dipped after Democrats won one hotly contested Senate race in Georgia on Wednesday and pulled ahead in a second.

A Democrat-controlled Senate would give more leeway to President-elect Joe Biden to act on his reform plans, which includes increased fiscal spending and possibly higher corporate taxes.

"Higher taxes would weigh on U.S. stocks. What we may witness in the coming months is that some investors may reallocate their funds away from U.S. assets," said Piotr Matys, emerging markets FX strategist at Rabobank.

"Emerging market assets may benefit from that."

Most emerging market (EM) currencies rose on that prospect, with the Russian rouble adding as much as 0.9%, as oil prices surged on bigger-than-expected Saudi output cuts.

However, some risk appetite for Russian assets was sapped after U.S. intelligence officials said Russia was likely behind a string of recent hacks on U.S. firms, driving stocks slightly lower.

Turkey's lira jumped 0.6% to the dollar on reports of increased lira holding by real money accounts. The lira has been on an uptrend ever since the central bank began hiking rates to combat double-digit inflation.

South Africa's rand lagged its peers as a locally originating coronavirus variant and mounting infections raised the possibility of renewed lockdown measures.

The country's national coronavirus command council is due to meet at 0700 GMT to decide on new measures.

Still, the rand and most other EM currencies have ridden a wave of optimism over an economic recovery this year, and are expected to further benefit from stimulus measures and the release of several coronavirus vaccines.

"Many countries have started vaccinations, and it's only a matter of time until this virus is under control, which will lead to recovery," Rabobank's Matys added.

EM stocks, which have benefited greatly from loose monetary policy and hopes of a recovery, edged up to their highest level since before the 2008 financial crisis.

Most EMEA stocks also rose, with Turkish stocks adding 0.8%, while South Africa's benchmark index gained 0.6%.

For GRAPHIC on emerging market FX performance in 2021, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2021, see https://tmsnrt.rs/2OusNdX

For TOP NEWS across emerging markets

For CENTRAL EUROPE market report, see

For TURKISH market report, see

For RUSSIAN market report, see (Reporting by Ambar Warrick in Bengaluru; Editing by Ramakrishnan M.)