Defeat meant West Indies have won just one of their last 28 Tests and saw England go an unbeatable 2-0 up in the four-match contest with just the final Test starting at the Riverside on Friday to come.
But a largely fledgling side, bolstered by the return from a knee injury of experienced batsman Shivnarine Chanderpaul, defied plenty of pundits by taking the match into the fifth day.
Set what would have been a Test record fourth innings victory total of 455, Chanderpaul's determined unbeaten 116 not out gave England more than a few scares before they sealed victory.
Just as encouraging for West Indies was the performance of debutant all-rounder Darren Sammy.
The 23-year-old, the first St Lucian to play Test cricket, bowled his medium-pacers with control to take seven for 66 in England's second innings, a haul which kept West Indies in the match.
For West Indies it was a major step forward after their record innings and 283 run defeat in the second Test at Headingley.
"After the loss at Headingley, we were written off in this series," said Ganga, captaining West Indies in a Test for the first time after skipper Ramnaresh Sarwan's tour ended with a shoulder injury at the Leeds ground.
"I think Shiv played a brilliant innings, one of the best Test match hundreds that I've seen. It's just unfortunate we couldn't go all the way.
"A lot of people doubted we could get 450," the opening batsman added.
"All credit to the guys and the manner in which they batted. Getting to 60 runs short of that total showed a lot of character and strength, and a lot of positives from this game we are going to take to that next Test."
Trinidad and Tobago captain Ganga has found himself involved in controversy after reports the selectors' choice of Chris Gayle as skipper for the upcoming one-dayers against England had been rejected by the West Indies Cricket Board.
It appears that Ganga, left on the sidelines during the recent World Cup in the Caribbean, could now captain the one-day side.
"There's a lot of speculation in the Caribbean," said Ganga. "These things are beyond my control. It's a stop-gap situation I've found myself in. This is a decision that has got to be made by the board."
Meanwhile Chanderpaul, himself a former West Indies captain, said he felt obliged to be an example to his younger colleagues.
"The senior players have to lead the way," said the 32-year-old left-hander. "The guys are still young and need some time to mature. I think when we get that right, we'll start winning some games."
And in the meantime Chanderpaul said he would continue to play through the pain barrier. "I've been doing a lot of hard work. The knee is painful, but I keep wrapping it up."