Shoppers who buy a four-pint bottle of own-label semi-skimmed milk can get 30p off their next purchase of Sainsbury's Woodland eggs via an on-pack voucher.
The promotion would enable Sainsbury's to avoid having to cut milk prices further, said experts, and would encourage spend in another category.
Cross-selling was "a smart way of engaging consumers on a value offering around their core shop," said Aidan Bocci, chief executive of Commercial Advantage. "These are absolute basics of why you go into a supermarket, so a large number of people will see the offer."
The move comes two weeks after Sainsbury's followed Asda and Tesco in reducing the price of four pints of own-label whole, skimmed and semi-skimmed milk from £1.53 to £1.25.
Morrisons reduced its prices the following day, with Waitrose following suit this week. The move is unusual for Waitrose, which had refused to engage in price-slashing tactics on staples such as milk and bananas to match its bigger competitors.