Shares of DuPont leapt on Monday after an influential shareholder advisory firm backed efforts by the activist investor Nelson Peltz to win seats on the industrial conglomerate’s board.

DuPont’s stock was up more than 4.5 percent by midafternoon, to $74.79, after Institutional Shareholder Services recommended that investors elect two of his four nominees, including Mr. Peltz, instead of two of the company’s directors.

The backing of I.S.S., the biggest proxy advisory firm, is a big win for Mr. Peltz and his Trian Fund Management as they engage in a bitter fight over the board of the company. The battle is one of the biggest this year between an activist shareholder and a stalwart of corporate America, as hedge funds and other investors seek to shake up companies.

On one side is DuPont, the chemical maker that traces its history back 213 years to a gunpowder manufacturing operation. On the other is Mr. Peltz, who has previously pressed for change at the likes of H.J. Heinz and PepsiCo.