Contract manufacturer Hon Hai and cameraphone lens maker Genius were both 7-percent limit up. Apple shares surged the most in more than three years on Jan. 25, after skyrocketing iPhone and iPad sales helped the company smash Wall Street expectations.
"What we are seeing today is a reflection of the Wall Street rally over the lunar new year holidays," said Bevan Yeh, a fund manager of Prudential Financial in Taiwan.
"However, concerns remain over the eurozone debt problems and the slowing US economic growth, leaving limited upside for Taiwan market."
Selling pressure is seen emerging at the 7,500 point level, some analysts said.
The main TAIEX index surged 173.72 points to 7,407.41, a level not seen since mid-November. The market had been closed from Jan. 19 for the holiday.
Among the biggest winning sectors, glass and electronics both jumped over 3 percent. Financial stocks gained 2.45 percent.
DRAM maker Nanya Technology was up 6.6 percent, the maximum allowed in a day.
Japan's Elpida Memory Inc aims to reach a deal as early as next month for a capital infusion from Micron Technology in a deal that could also include Nanya, Japan's Nikkei business daily said last week.
Nanya's chairman said on Monday however there was no current plan to take part in any deal.
The Taiwan dollar was up by T$0.25 to trade at T$29.74.
Foreign investors were net buyers on Jan. 18, the last session before the holiday, bringing their total buying to T$27.9 billion this month.