Twente went down to a surprise 2-1 defeat at home to second division side FC Den Bosch in midweek but hit back with an emphatic 3-0 defeat of Ronald Koeman's Rotterdammers.
Nacer Chadli put them ahead after nine minutes and Luc Castaignos added a second against his former club eight minutes later.
Feyenoord pushed for a route back into the contest but Dusan Tadic killed their hopes with a third 12 minutes from time.
Former England manager McClaren, in his second spell in charge of the Enschede outfit, told the club's official website: "It was a tough, tough game for us, not only physically but also mentally.
"We said we had to win the big games and this was one of those.
"The players fought hard, were organised and scored at the right times.
"It was a good reaction after the disappointment of midweek, both on and off the field.
"The fans can have a major impact and they were great."
Koeman was underwhelmed by his side's display.
The former Holland defender said: "We played nicely today but nice is not enough.
"We missed the last 10 per cent needed to win these games.
"Both defensively and offensively we lacked belief and this is what decides these kind of matches."
NEC Nijmegen moved up to seventh after substitute Geert-Arend Roorda grabbed a last-minute winner at FC Groningen.
Michael De Leeuw put the home side ahead after 11 minutes but Victor Palsson equalised 20 minutes into the second half before Roorda's last-gasp strike settled it.
Heerenveen beat PEC Zwolle 2-1 with goals from Alfred Finnbogason and Daniel De Ridder. Joey van der Berg scored an 87th-minute penalty for Zwolle to give them late hope but they could not find an equaliser.
RKC Waalwijk squandered an early lead to lose at NAC Breda.
Teddy Chevalier put RKC ahead in the second minute but NAC hit back to claim the three points with goals from Danny Verbeek and Nemanja Gudelj.
VVV-Venlo produced arguably the performance of the day to claim their first Eredivisie win of the season - a 2-1 success at AZ Alkmaar.
The visitors went ahead after Barry Maguire finished off a lovely passing move with a close-range finish after 78 minutes.
AZ levelled through Erik Falkenburg's tap-in with three minutes to go but VVV grabbed an injury-time winner when Aleksandar Radosavljevic capped a swift counter-attack with a crisp finish.