Benchmark zinc ended up 0.4 percent at $2,833 a tonne. Earlier, prices of the metal used to galvanise steel touched $2,874.50, the highest since March 30.
"We've had a large drawdown in stocks. Investors have turned positive on industrial metals since China's June manufacturing PMI came out," Capital Economics analyst Caroline Bain said.
"We expect a 185,000 tonne deficit this year and a balanced market next year ... There are signs supply will improve."
INVENTORIES: Stocks of zinc in LME warehouses at 273,675 are down more 35 percent since the start of the year. A tight market is exacerbated by cancelled warrants - metal earmarked for delivery - at nearly 75 percent.
SPREADS: Worries about supplies on the LME market are highlighted by the discount for cash over the 3-month forward, which has narrowed to near zero from around $20 a tonne in mid-June.
SHANGHAI STOCKS: Zinc inventories in warehouses monitored by the Shanghai Futures Exchange have plummeted more than 50 percent to below 67,000 tonnes since January.
DEMAND: China accounts for nearly half of global demand estimated at around 15 million tonnes this year.
DEFICIT: the International Lead and Zinc Study Group (ILZSG) said in April the zinc market was expected to see a deficit of 226,000 tonnes this year.
FUTURE SUPPLY: "New large mines in Australia and South Africa will add 460,000 tonnes of supply by 2019," Liberum analysts said in a note. "Slowing Chinese credit growth should bring implied steel demand back into negative territory. Zinc consumption should come under similar pressure given the high correlation."
CHINA: China's manufacturing engine cranked up in June, expanding at the fastest pace in three months, as new orders and production rose in a sign of a modest recovery.
ALUMINIUM: Expectations of higher supplies to come to the LME market have seen the discount for cash over the three-month contract widen to above $16 a tonne, the highest since February, from near $4 a tonne at the end of June.
ALUMINIUM STOCKS: Latest LME data shows stocks rose 14,875 tonnes to above 1.39 million tonnes. Three-month aluminium slid 0.6 percent lower at $1,889.
ALCOA: Weighing on aluminium was news that Alcoa would partially restart its Warrick smelter in Indiana.
CHINA DATA: Industrial metals were also boosted by Chinese banks extending more credit than expected in June.
PRICES: Copper closed 0.5 percent higher at $5,905 a tonne, lead gained 0.9 percent to $2,327, tin rose 0.6 percent to $19,900 and nickel added 0.9 percent to $9,210 a tonne.