Newcastle were already facing a tricky afternoon after Bafétimbi Gomis had given the hosts an eighth-minute lead but life was made harder when Janmaat was dismissed just before the break for two bookings for fouls on Jefferson Montero.
Andre Ayew notched his second goal in his second game for Swansea to wrap up the points on 52 minutes in a game which also saw Garry Monk’s men twice hit the woodwork.
Both sides came into the contest fresh from positive performances in respective 2-2 draws on the opening weekend but it was Swansea, rather than the Newcastle, that kept up that momentum in the early stages.
Jonjo Shelvey was at the heart of most good early work by the hosts and it was his vision in midfield that provided the opening goal.
On eight minutes the former Liverpool man split the two Newcastle centre-backs with a wonderful pass that sent Gomis through on goal and after rounding Tim Krul with ease, the striker tapped the ball into the empty net.
Newcastle had an obvious plan to get tight to the lively Montero in the early stages but Jaanmat took that a little too far by crunching into him from behind on 17 minutes deep inside the Swansea half. It was a needless foul and booking that would cost the visitors dear later in the half.
Although they didn’t create any meaningful chances, Newcastle, through Moussa Sissoko, were slowly starting to pen the hosts in and Gabriel Obertan tested Lucas Fabianski with a low shot that required a good save down to his right.
With half-time approaching they were well in the game but their task of staging a comeback was made much more difficult on 40 minutes when Jaanmat picked up his second yellow card.
Montero had already drew another foul from the Toon full-back to put him on a tightrope before the Dutch defender pulled Montero back as he drove forward to leave the referee little choice but to brandish a second yellow.
The dismissal gave Montero more space to work and he smacked the post just before half-time with a fierce 20-yard drive.
Steven Taylor replaced Sissoko at the break as Steve McClaren tried to nullify the space that Montero was exploiting but his plan failed.
The winger danced his way down the left-flank on 52 minutes and delivered a pin-point cross for Ayew to powerfully head home and seal the points.
That goal killed the game as a contest and Gylfi Sigurdsson came very close to adding a third on 59 minutes but his 25-yard drive cannoned back off the crossbar.
Soccer Saturday verdict – Matt Le Tissier
It is never easy when you go down to the ten men. Especially the forwards when you know you’re going to get very little service from there on in.
[Cisse] was not really in the game at all before Newcastle went down to 10 men but it was just poor all round. We didn’t see much of Wijnaldum today, but not too many Newcastle players will have come out of that with too much credit.
Newcastle have got some good players in the side and I’m sure when Steve McClaren gets it to click it will be a lot better.
Swansea: Fabianski (7), Naughton (7), Fernandez (7), Williams (7), Taylor (7), Cork (7), Shelvey (8), Sigurdsson (7), Ayew (7), Montero (8), Gomis (7).
Subs: Dyer (6), Routledge (6), Britton (6).
Newcastle: Krul (6), Janmaat (3), Mbemba (6), Coloccini (5), Haidara (6), Anita (6), Colback (6), Sissoko (7), Wijnaldum (5), Obertan (6), Cisse (5).
Subs: Taylor (6), Aarons (6), Mitrovic (5)
Man of the match: Jonjo Shelvey