An analyst cautioned, however, that soaring power prices are also likely to hit industrial output, crimping demand for metals.
"We should not forget that not only the primary metals producers are being hit by the power crunch, but also the metals manufacturers, the ones further down the value chain," said Daniel Briesemann at Commerzbank in Frankfurt.
"At the moment, everyone apparently wants to see higher prices, so they are focusing on just one side of the equation."
Benchmark zinc CMZN3 on the London Metal Exchange climbed 3.3% to $3,369 a tonne in official trading, the strongest since March 2018.
The most-traded November zinc contract on the Shanghai Futures Exchange closed up 1.5% at 24,000 yuan ($3,721.68) a tonne, its highest since November 2007.
"Chinese (zinc) smelters have cut production for several times in the past months, and we have revised down the production forecast by 80,000 tonnes compared with our previous forecast in early 2021," said CRU analyst Dina Yu in Beijing.
The global zinc market will be slightly over-supplied this year and next, the International Lead and Zinc Study Group said on Tuesday.
* Aluminium, the most power intensive base metal, gained 0.7% in LME official rings to $3,088 a tonne after hitting the highest since July 2008 at $3,118.50.
* China's copper imports in September snapped a run of five month-on-month declines, data showed.
* LME copper added 1% to $9,559.50 a tonne, nickel rose 1.1% to $19,185, lead advanced 1.5% to $2,244 while tin dipped 0.1% to $36,450 a tonne.
($1 = 6.4487 yuan)
(Additional reporting by Mai Nguyen in Hanoi, Editing by Louise Heavens) ((email@example.com; +44 20 7542 7093; Twitter https://twitter.com/reutersEricO; Reuters Messaging: firstname.lastname@example.org))