TOKYO—Japanese government bond yields sank to their lowest-ever level Thursday, defying an upswing in U.S. yields over the last week and demonstrating the Bank of Japan ’s overwhelming influence on the market.

The benchmark 10-year Japanese government bond was yielding just 0.31% in afternoon trading, meaning investors were willing to accept just above ¥3 of interest annually for every ¥1,000 invested. The previous low yield of 0.315% was set in April 2013.

Yields on shorter-term Japanese government debt are even lower, or nonexistent. On Thursday, the government auctioned two-year bonds and for the first time received a negative yield—in other words, investors were paying the Japanese government to take their money. The Finance Ministry sold ¥2.7 trillion ($22.41 billion) of two-year bonds for a yield of minus 0.003%.

The Bank of Japan has unleashed two rounds of monetary easing to flood financial markets with cash, the first in April 2013 and the second in October 2014. After the first round, the central bank was vacuuming up the equivalent of 70% of newly issued bonds. Now it is cleaning up the equivalent of all new government bond issuance, although it always buys on the secondary market to avoid the impression that it is directly underwriting government debt.

The BOJ hopes to spark 2% inflation and prod big investors to look to riskier assets, and by one measure it has succeeded: The Nikkei Stock Average has surged nearly 14% since the October action.

Traders say that with the central bank’s dominant role in the Japanese government bond market—sometimes likened to a giant whale in a pond—many market participants are reluctant to bet on a rise in yields.

Japanese government bonds give investors little reward compared with U.S. government bonds. The benchmark 10-year Treasury yielded 2.265% as of Tuesday afternoon.

“External factors don’t matter much,” said Satoshi Yamada, senior quantitative analyst at SMBC Nikko Securities. “With the BOJ expected to keep steadily snapping up JGBs well into the next year, there is almost no chance of rates going higher soon.”

That is despite concerns expressed by some foreign investors that Japan’s government debt—which is more than twice the size of the economy—may be too large to handle. Moody’s Investors Service on Dec. 1 downgraded Japan’s credit rating, citing heightened concern over the nation’s ability to cut its budget deficit. The downgrade sparked a small rise in yields that was over in almost the blink of eye. Since then, yields have steadily moved downward.

“It wouldn’t be surprising to see the benchmark 10-year yield dip below 0.30%,” said Mr. Yamada, adding that such a fall could come into view sometime in the first half of next year before the U.S. Federal Reserve moves to raise short-term rates.

“The fall in yields appears to be prompted by fresh moves from investors who need to buy at the end of the quarter or to make up for a decrease of JGB holdings in their portfolios caused by the Finance Ministry’s bond redemption this month,” said Mari Iwashita, chief economist at SMBC Friend Securities. She said slow trading during the Christmas season might have exaggerated price movements.

—Hiroyuki Kachi contributed to this article.

Write to Tatsuo Ito at tatsuo.ito@wsj.com