Following a first set which saw six breaks of serve – four of them by the British team – the second was much more straightforward for the perennial champions, in spite of the conditions.
It capped a slightly odd day for Reid and Hewett, which they started as opponents in the singles quarter-finals.
Hewett, the second seed, triumphed 6-2 6-4. He will play fourth seed Fernandez in the singles semi-finals.
Elsewhere, Britain’s Andy Lapthorne suffered double elimination in men’s quad wheelchair events on Thursday.
The Englishman’s day started with a 6-4 6-4 defeat in the singles semi-final to top seed Niels Vink of the Netherlands.
He then suffered another last-four loss in the doubles as, along with Dutch partner Sam Schroder, he was beaten in the match tie-break by Ahmet Kaplan of Turkey and South Africa’s Donald Ramphadi, losing 6-3 2-6 10-7.
Lapthorne and Schroder, the second seeds, fought back from losing the first set by winning the second in 35 minutes, and were ahead in the first-to-10 shootout decider before suffering defeat against their unseeded opponents.