The Dow was also more than 80 points above its all-time closing high of 14,164 set on October 9, 2007.
The broad-based S&P 500 picked up 11.19 (0.73%) to 1,536.39, still shy of its closing and intraday records also set in October 2007.
The tech-rich Nasdaq Composite Index gained 26.65 (0.84%) to 3,208.68.
"This is something that's been building for months and months," Chris Low, chief economist at FTN Financial, said of the record.
"It's always significant, particularly significant because this economic cycle has been so challenging," Low said.
Tuesday's surge came on the heels of rising markets in China and throughout Europe, Low pointed out.
But he predicted the Dow would have trouble keeping its upward momentum in the coming months because of the effects of the US payroll tax increase and the federal spending cuts known as the sequester.