More than an hour into a bitter, 90-minute debate that often devolved into inexplicable interruptions and trivial jabs more notable for political animus than policy substance, President Trump and former Vice President Joseph R. Biden Jr. sparred over climate change and energy.

During the first of three scheduled debates Tuesday night at Case Western Reserve University in Cleveland, the Republican incumbent and Democratic nominee were pressed by Fox News anchor and moderator Chris Wallace to make clear their respective positions on “the science of climate change.”

What followed in a roughly 10-minute exchange did little to amplify the policy positions of either candidate. However, the discussion did punctuate a sharp divergence between the two — both their worldviews and...