Democratic Senate candidates hold large fundraising advantages over Republicans as they begin to build an edge in the race to control the upper chamber this November, with some crediting the wave of blue money to June’s Dobbs v. Jackson abortion decision from the Supreme Court.

In Ohio, the Republican nominee, J.D. Vance, is trailing the Democratic nominee, Congressman Tim Ryan, in the fiscal race, with about $625,000 in his coffers compared to Mr. Ryan’s more than $3.5 million.

The GOP nominee in next-door neighbor Pennsylvania, Mehmet Oz, is trailing Lieutenant Governor John Fetterman, a Democrat, in funds as well — $1.1 million to $5.5 million.

A survey of competitive Senate races shows that Democrats enjoy big financial advantages in North Carolina, Georgia, and Nevada as well. The exception is Wisconsin, where Senator Johnson, the incumbent, has more than double his Democratic challenger’s funds.

The starkest example of the Democratic financial advantage is in Arizona, where Senator Kelly has about 16 times as much money as his opponent, venture capitalist Blake Masters. Mr. Kelly enjoys a war chest just shy of $25 million, while Mr. Masters has about $1.5 million

A data scientist at Decision Desk HQ who is a professor at Washington University at St. Louis, Liberty Vittert, says the wave of Democratic money is “pushing our current projections that the Democrats are going to win the Senate.”

Ms. Vitteret says money used to be king in American elections, but that’s not the case any more, citing President Trump’s 2016 win as evidence. She is, however, doubtful that the current slate of GOP nominees will be able to replicate Mr. Trump’s success, saying “you just can’t draw parallels.”

Nationally, the Democratic and Republican senatorial committees have raised similar amounts of money — $163 million and $173 million, respectively — according to August Federal Elections Commission data.

Republicans, however, spent much more of their money battling it out in competitive primaries, often between Trump-supporting and Trump-opposing candidates. The GOP’s Senate arm only has about $28.5 million left, whereas Democrats have more than $52.5 million still on hand.

Each senatorial committee’s funds represent a modest increase from the 2018 midterms, when both partisan committees raised around $150 million. According to Ms. Vittert, the trends show that Republicans aren’t raising less money than usual, but rather that Democratic candidates are raising more than expected.

She credits the Dobbs v. Jackson decision for the swing in the Democrats’ direction, noting that their chances of retaining the Senate and maintaining their edge in the generic ballot polling average, which measures popular partisan support, have improved since the ruling in late June.

On June 24, the day the ruling was handed down, Real Clear Politics’ average of generic ballot polling, which incorporates dozens of polls, showed Republicans leading 44.7 percent to 41.3 percent.

In the past month and a half, the gap has closed to a virtual tie, with Real Clear Politics reporting an average of 44.3 percent support for Republicans and 44.2 percent support for Democrats.

“Dems are slowly consolidating their lead in the states where they’re leading,” Ms. Vittert said. “There’s no doubt that a huge amount of the fundraising that Dems have done is off Roe v. Wade.”

In the battle for the House, the fundraising has not been as lopsided, with the Democratic and Republican congressional committees raising $239 million and $215 million, respectively.

As it stands now, the GOP is still favored to take the lower chamber, with most forecasts expecting them to control about 230 seats after the November elections.