Yoan Gouffran's 36th-minute header put the hosts ahead before Chris Brunt levelled with his first goal since last January early in the second half.
But Frenchman Sissoko crashed home the winner just before the hour mark.
The Baggies gave as good as they got in an end-to-end encounter which often lacked quality, but not effort and commitment, in front of a crowd of 49,298.
The Baggies started the better and Newcastle keeper Tim Krul had to make a smart save to turn Brunt's curling free-kick around the post.
However, the Dutchman was less than convincing when the resulting corner was delivered and it took a brave block by returning full-back Mathieu Debuchy to prevent Stephane Sessegnon from capitalising from close range.
The home side gradually worked their way into the game, although with Republic of Ireland striker Shane Long causing all kinds of problems for Fabricio Coloccini and Mike Williamson as the Baggies launched an aerial assault, there was little to choose between the teams.
Loic Remy, who went into the game with eight goals in as many league appearances, was strangely off colour and failed to make the most of Debuchy's inviting 19th-minute cross, glancing a header tamely towards goal which defender Billy Jones was able to clear.
However, it was Alan Pardew's men who eventually took the lead nine minutes before the break when they scored from a corner for the second time in a week having gone more than two years previously without having done so.
West Brom keeper Boaz Myhill made a mess of punching Yohan Cabaye's left-wing corner clear, sending the ball straight up into the air and as it dropped, Gouffran got there first despite the best efforts of Youssouf Mulumbu and headed into the empty net.
Albion spurred on
The setback spurred the visitors on once again, although Sessegnon, who had earlier shot tamely at Krul, sliced an attempt horribly wide from the edge of the penalty area.
Newcastle left the pitch feeling aggrieved after defender Jonas Olsson appeared to drag back Remy when he had been played through by Cabaye.
The incident took place outside the box, but had he blown, referee Phil Dowd, who opted not to red card Everton's Kevin Mirallas last weekend, might have had little option but to do so this time around.
Albion were level with 53 minutes gone when Brunt picked up possession beyond the far post and took a touch before smashing the ball left-footed past Krul and in off the underside of the bar.
It might have been even worse for the Magpies three minutes later when Long failed to connect with Olsson's header down from Morgan Amalfitano's corner.
The third goal of the game came at the other end within seconds when Remy headed the ball into the path of Sissoko and he blasted an unstoppable shot into Myhill's top-left corner.
Newcastle stepped up a gear in a bid to wrap up the win and might have done so had Debuchy not thumped a shot straight into Myhill's midriff after latching on to the keeper's poorly-aimed throw.
But substitute Victor Anichebe headed just wide in the final minute of normal time as the visitors came desperately close to snatching a point in a late flurry which prompted heroics from Williamson and Debuchy in particular.