The Magpies led 3-0 with 47 minutes gone and looked to be cruising to victory with Steven Taylor's 16th-minute strike, a second from Peter Lovenkrands and a Jonas Olsson own goal looking to have secured a victory.
But Tchoyi reduced the deficit with a 62nd-minute strike and when he added a second 10 minutes later, nerves were jangling on Tyneside.
However, the Cameroon international midfielder was not done and with seconds of normal time remaining, powered home a diving header to deny the Magpies a top-10 finish in front of a crowd of 51,678.
Perhaps even more disappointingly, it meant that the Magpies finished below arch-rivals Sunderland, whose victory at relegated West Ham lifted them into 10th place, two positions better off.
It is a measure of how well both Newcastle and West Brom have coped with their return to the top flight that they headed into the final game of the season already safe and bidding for a place in the top half of the table, something few outside their respective dressing rooms would have predicted before a ball was kicked.
But while there was nothing crucial at stake, both set about the task of bringing successful campaigns to a winning conclusion, and it was the Magpies who took the initiative during a first 45 minutes which grew in intensity the longer it went on.
In a lively start, Scott Carson had to clutch a third-minute Shane Ferguson drive to his chest and opposite number Tim Krul was relieved to find Steven Taylor in the right place at the right time four minutes later to intercept Marc-Antoine Fortune's shot on the line after Jose Enrique had gifted possession to Tchoyi.
But as the half wore on, it was the home side which started to press on a more sustained basis, and they took the lead with 16 minutes gone.
The Baggies made a mess of dealing with Ryan Taylor's inswinging corner and when Lovenkrands helped the ball back into the six-yard box, Steven Taylor turned Youssouf Mulumbu to fire home from close range.
Newcastle gradually increased the tempo and after Danny Guthrie had fired just over from distance and Steven Taylor had headed wide, they went further ahead six minutes before the break with a helping hand from Carson.
Lovenkrands ran on to Ameobi's header and attempted to lift the ball over the keeper, who got a glove to it and then caught it as it dropped behind him, but his frantic efforts to persuade the officials that it had not crossed the line fell on deaf ears.
The visitors continued to enjoy their fair share of possession, but it was simply not their day in the first half. Three minutes before the break Fortune's goal-bound effort was again blocked on the line by Steven Taylor, whose clearance hit Krul and ran to safety.
Carson had to beat away another Guthrie piledriver seconds later as an entertaining half drew to a close with the Magpies firmly in control.
They tightened their stranglehold within two minutes of the restart with the visitors once again contributing to their own downfall.
Jose Enrique's cross towards the near post fell nicely for Olsson to clear, but he sliced the ball past the helpless Carson and into his own net to extend Newcastle's lead to 3-0.
The visitors continued to battle gamely for a way back into the match, but the Magpies were enjoying themselves as they stroked the ball around comfortably.
However, West Brom did break their duck with 62 minutes gone when Tchoyi beat the offside trap to run on to a ball over the top and calmly slide his shot past Krul.
Alarm bells were ringing in the Geordie ranks 10 minutes later when Tchoyi stepped inside Fabricio Coloccini and blasted home his side's second to make for a tense final few minutes.
The rescue mission was complete in the final minute of normal time when Olsson crossed from the left for Tchoyi to snatch a point with a diving header.