Trump, who appeared at a campaign rally for Strange last week, congratulated Moore on his win and wished him success against Democrat Doug Jones in the December special election to fill the seat held by Jeff Sessions before he became United States Attorney-General in February. Strange had been appointed to fill the seat until the election.
"Congratulations to Roy Moore on his Republican Primary win in Alabama. Luther Strange started way back & ran a good race. Roy, WIN in Dec!" Trump wrote on Twitter.
Establishment Republicans have been wary of insurgent firebrands since the 2010 congressional elections. That year, donations from conservative groups helped bring about primary wins by ultra-conservative candidates Christine O'Donnell in Delaware and Sharron Angle in Nevada. But both suffered crushing defeats to Democrats in the general election.
In November 2018, elections will be held for all 435 seats in the US House and 33 seats in the 100-member Senate, including 23 Democrats and eight Republicans in fights that will likely be cast as a referendum on Trump's legislative agenda.
The Republican establishment poured millions of dollars into the Alabama nominating primary to help Strange, giving him a US$10 million money advantage over Moore.
Some Republican strategists fear that if more extreme Republicans win primaries, it would give Democrats a better chance of winning in the general election.
That is less of a concern in conservative Alabama, where Moore will likely prevail, but is a bigger risk in states with greater numbers of moderate voters, such as Arizona and Nevada, where Republican Senators Jeff Flake and Dean Heller are already top targets for conservative groups.
Also this week, Republican Senator Bob Corker of Tennessee said he would not run again in 2018, a decision that was widely seen as trying to avoid a potential primary fight.
"I know we are all listening and watching very closely, trying to understand the message that's being sent," Senator John Cornyn of Texas, the No 2 Senate Republican, said of the Alabama result.
While Trump endorsed Strange, his former adviser Steve Bannon backed Moore, as did several outside political groups that support the President's agenda.
Bannon, and his influential news site Breitbart, are poised to spearhead attacks on Republican incumbents, while political groups aligned with Trump that can raise unlimited sums of money will help those challengers compete with better-financed establishment candidates.
Having served as a high-profile state Supreme Court justice for years, Moore was better known than most insurgent candidates, allowing him to neutralise attacks from establishment groups, said Constantin Querard, a conservative Republican strategist in Arizona.
The road will be tougher for outsiders in Arizona and Nevada, he said. Still, candidates such as Flake will be hampered by their ties to the Washington establishment, especially with the failure this year by Republicans to deliver on long-standing promises to repeal the Obamacare healthcare law despite controlling the White House and Congress.
Querard said that Flake "is seen as the poster child for everything that is wrong in Washington".
Jonathan Gray, a Republican consultant in Alabama, said Moore's win should frighten vulnerable Republicans worried about primary challenges not so much because Trump's endorsement failed to sway voters, but because the money spent at the behest of Senate Majority Leader Mitch McConnell to back Strange was fruitless.
"The people of Alabama saw Washington telling them what to do, and they thumbed their nose at it," Gray said.
