PSV have 36 points from 16 matches, two ahead of Twente and Vitesse Arnhem, who suffered their first away defeat since March when they went down 3-1 at lowly VVV Venlo.
Wijnaldum opened the scoring seven minutes before the break from close range but Twente stayed in contention until late goals by Matvz and Narsingh secured the points after PSV had earlier wasted several chances to wrap up the victory.
"We played aggressively and created enough chances to clinch a fully deserved win," said Dick Advocaat whose PSV side had lost their previous two matches against Vitesse Arnhem and Ajax Amsterdam.
"But missing so many chances kept Twente in the match and even close to an equaliser. That has to improve and my team knows that."
Twente coach Steve McClaren added: "We knew that there was pressure on PSV and then you need the will to win and also the belief and mentality but we lacked both today and that was very disappointing."
Wijnaldum, whose goal was created by winger Narsingh, missed two more chances in the second half when he shot wide from inside the area and then saw his effort cleared off the line by Roberto Rosales after good work from Jeremain Lens.
Matavz finally doubled the lead in the 80th minute from Kevin Strootman's defence-splitting pass and Narsingh chipped the third goal two minutes later when he combined with Matavz to seal PSV's first home win over Twente since 2007.
Marco van Ginkel put Vitesse ahead at Venlo after 10 minutes but Yuki Otsu equalised when he netted a rebound five minutes before the break and second-half goals by Bryan Linssen and Robert Cullen earned the hosts their third win of the season.
The win took Venlo out of the relegation zone and up to 15th place in the 18-team standings with 14 points.
Ajax beat Groningen 2-0 on Saturday to remain fourth with 33 points, two ahead of Feyenoord who were held to a 2-2 draw on Sunday by struggling NAC Breda who twice came from behind in a match that saw both sides finish with 10 men.
Graziano Pelle put Feyenoord ahead after five minutes with his 11th league goal of the season but Kees Luijckx equalised in the 23rd before Darryl Janmaat was sent off six minutes later after two bookings in two minutes.
Feyenoord's Lex Immers converted a penalty in the 74th after Eric Botteghin held Pelle and got a second booking but two minutes later Nemanja Gudelj's close-range header salvaged a point for Breda who are third from bottom with 13 points.