"The rebound in the tech sector last week was not big and investors who thought tech shares had been oversold recently continued to add holdings," said Albert Lin, vice president at Hotung Securities.
Reflecting growing confidence among investors, turnover spiked to a 6-week high of T$99.83 billion from the last session's T$63.65 billion.
TSMC, the market's most heavily weighted stock, jumped 4.0 percent to T$52.00, pushing the electronics sub-index up 2.44 percent.
The firm said the worst of an inventory glut in the semiconductor industry would be over in the first quarter.
The gains came after TSMC said on Sunday it had settled a patent and trade secret suit with Semiconductor Manufacturing International Corp (SMIC) and the Chinese rival would pay it US $175 million over 6 years. Display screen makers were among the best performers.
AU Optronics Corp, the world's third-largest display maker, gained 5.92 percent to T$48.30 even though the tech-laced US Nasdaq fell 0.55 percent on Friday.
AU and its smaller Taiwan rivals are widely expected to report fourth-quarter losses, but upbeat investors are betting that prices of liquid crystal displays would hit bottom soon.
However, investors shunned some major tech exporters on worries that a stronger Taiwan currency may have caused foreign-exchange losses in the fourth quarter.
Laptop computer maker Compal Electronics Inc fell 0.33 percent to T$30.0, for example.
On the non-tech side, investors piled onto transport shares after historic charter flights between Taiwan and China over the weekend raised hopes for permanent air links and better ties.
China Airlines, the island's top air carrier, closed up 1.71 percent at T$17.80 and shipping firm Evergreen Marine jumped 5.56 percent to T$30.40.
The over-the-counter market's TAISDAQ index added 2.03 percent to close at 112.70, and February TAIEX futures rose 1.84 percent to end at 5,982.