Money continued to flow to sectors seen as likely to benefit from the Republican triumph on Tuesday, which is expected to block Democratic-led efforts to tighten regulations on banks and cap drug prices.
JPMorgan Chase jumped 4.7 percent and Pfizer rose 3.0 percent. Caterpillar, which is expected to prosper from ramped-up public works spending, rose 2.7 percent.
About 25 minutes into trade, the Dow was at 18,757.78, up 0.9 percent and 120 points above the all-time closing high.
The broad-based S&P 500 rose 0.7 percent to 2,177.75 while the tech-rich Nasdaq Composite Index advanced 0.7 percent to 5,287.53.
Leading US stock indices have risen four days in a row, after a nine-day slump.
Briefing.com analyst Patrick O'Hare described a "bandwagon momentum trade" that was supported in part by a shift in funds from the bond market to equities in anticipation of a large spending program under Trump.
"This morning the afterglow of Wednesday's rally, which annihilated conventional wisdom, has fostered a warm, fuzzy feeling that the equity market could be poised to enjoy a year-end rally driven by underexposed money managers playing catch-up, and the unwinding of safe-haven (and crowded) trades in the Treasury market finding a place in the stock market," O'Hare said.