Kinnear was not present for Saturday's encounter after being taken to hospital due to illness ahead of the crucial fixture in the Midlands and assistant Chris Hughton was in charge.
The Magpies, though, showed no signs of missing their boss as they rushed into a lead in the opening 64 seconds against rock-bottom West Brom when Damien Duff took advantage of terrible defending from Leon Barnett to slot past Scott Carson.
However, West Brom - who could have overtaken their visitors with victory - immediately hit back as Newcastle's Steven Taylor slipped to allow Marc-Antoine Fortune to smash a fourth minute equaliser.
The scores remained level for only five minutes as Newcastle again took the lead when West Brom failed to clear and Peter Lovenkrands was allowed to hit his first goal for his new employers on his first start.
But that was not the end of the first-half action as, with four minutes remaining before the interval, Steven Taylor atoned for his earlier error when capitalising on more adrift Baggies defending to head in a corner from debutant Ryan Taylor.
Fortune set up a tense ending with West Brom's second on 74 minutes, but Tony Mowbray's side never truly looked capable of salvaging a point.
Newcastle got off to a dream start by taking the lead through the excellent Duff in only the second minute, following a mistake from Barnett.
StumbleShola Ameobi tried to pick out the run of Duff. Barnett should have cut out the pass, only to stumble and allow the winger a clear run at goal. Duff had all the time in the world to steady himself before drilling past Carson.
The home side quickly retaliated and in the fourth minute drew level through Fortune. Nicky Butt gave away possession and this was seized upon by Albion playmaker Borja Valero, who threaded the ball through to Fortune.
He took advantage of a slip on the edge of the box by Steven Taylor and fired a low shot past Steve Harper into the corner of the net.
Lovenkrands restored Newcastle's lead after nine minutes, volleying in from 15 yards after Butt's cross was hit back across goal by Ryan Taylor.
Fabricio Coloccini came to Newcastle's rescue when he blocked a goal-bound shot from James Morrison after good play by Valero, who had shepherded the ball away from Harper.
But the fragile nature of the Baggies defence meant Newcastle always looked capable of scoring when they ventured forward.
Ryan Taylor would have been disappointed not to have at least hit the target when he dragged a shot wide from 15 yards out when in space.
But the Albion defence was non-existent when Steven Taylor stretched Newcastle's lead after 41 minutes.
ControversialRyan Taylor's corner flew straight across the box with Abdoulaye Meite ball-watching as Steven Taylor sent a glancing header into the corner of the net.
Mowbray made a double substitution at the start of the second half with Roman Bednar and Filipe Teixeira replacing Chris Brunt and Kim Do-Heon, respectively.
Morrison was not too wide of the mark with a curling 20-yard effort but the Magpies looked relatively comfortable in protecting their advantage.
Duff came close to making it 4-1 with an angled drive which flew just past the far post after he had dispossessed Carl Hoefkens.
Barnett and Kevin Nolan were booked after confronting each other, with the Newcastle midfielder unhappy with a challenge on Ameobi, who needed treatment.
With 74 minutes on the clock Albion reduced the arrears in controversial circumstances.
Bednar was down injured and Newcastle players were urging the home side to kick the ball out of play so he could receive treatment.
But Albion played on and Robert Koren slipped the ball through to Fortune, who hammered home his second goal of the game.
Valero came close to making it 3-3 when his glancing header from a Robinson cross flew just wide - but the Magpies held on for victory.
West Bromwich Albion
1st Half Goals
Shots on Target
Shots off Target