Diego Valeri put Portland ahead after just 27 seconds when he charged down a clearance from keeper Steve Clark.
Rodney Wallace then headed in to make it 2-0 in the seventh minute.
Kei Kamara pulled one back before half-time but the Timbers won their first major trophy since joining MLS in 2011.
Portland captain Ridgewell, 31, who played in the Premier League for Aston Villa, Birmingham City and West Bromwich Albion, is in his second season with the club.
The final, at the Crew's Mapre Stadium, got off to a dramatic start when Clark's error gifted Valeri the opening goal.
The keeper's attempted clearance bounced off the Argentine and into the net, to set a new record for the fastest goal in the history of the MLS Cup - the name given to the final.
Portland were then gifted another goal when they were allowed to play on after the ball had clearly gone out for what should have been a throw-in, and Lucas Melano crossed for Costa Rica international Wallace to head in.
Columbus hit back as their top scorer, Sierra Leone forward Kamara, fired in his 26th goal of the season on the turn after goalkeeper Larsen Kwarasey had spilled a cross.
But the hosts barely made another chance as Ridgewell's defence stood firm and Portland were unfortunate not to add to their lead in the second half as they created a number of chances.
Melano saw a shot blocked, Kamara was spared an own-goal by Michael Parkhurst's goalline clearance, Fanendo Adi headed against a post and Clark saved superbly from Natt Borchers' close-range header.

Hamilton struggled to fourth behind the Ferraris of title leader Sebastian Vettel and Kimi Raikkonen while team-mate Valtteri Bottas took a maiden win.
Hamilton said: "Big congratulations to Valtteri. Fantastic job and he deserves the win. He has been fast all weekend.
"For me, just a very, very odd weekend. I am just hopeful in the next races I will be able to pick up the pace."
Bottas' win ensured the damage to Hamilton in the championship was limited as much as possible - Vettel now leads by 13 points but it would have been 20 had the German won the race.
"It's great we are ahead of the Ferraris," the Briton said. "It has stopped Sebastian pulling away too far."
Hamilton was more than half a second slower than Bottas in qualifying and as the Finn made a blistering start from third and took the lead at the first corner, Hamilton did not make ground from fourth on the grid.
The 32-year-old suffered overheating problems as he chased Raikkonen in the first stint of the race and dropped back over the pit-stop period to finish 25 seconds behind the Finn and 36 behind Bottas.
"I don't remember the last time we had that [overheating]," Hamilton said. "It meant I was out of the race from the get-go.
"I think I had the pace to fight with Kimi but the car was just overheating the whole the time. I'm sure we will go back to the drawing board and figure it out."
Bottas joined Mercedes over the winter following the retirement of world champion Nico Rosberg.
Bottas said his first win felt "surreal", but added: "It's a good feeling and I am happy."
He added: "I always knew I could get good results if everything goes right and I always trust in my ability. But it's nice to get confirmation that the results are possible.
"It took quite a while, more than 80 races for me, but it's definitely worth the wait. This strange opportunity came to me in the winter to join the team and they made it possible, so I want to thank them."
Bottas moves into third place in the championship, 23 points behind Vettel and 10 behind Hamilton.
He said: "[Winning the title] has always been the only goal for me in my career but I have not had the chance to prove it. Now I have the chance to prove I can win races and titles. Two weeks ago people were saying I am the number two driver but today it looks very different."
Portland Timbers became Major League Soccer champions for the first time as they beat Columbus Crew in the final, with ex-Premier League defender Liam Ridgewell lifting the trophy.
[NEXT_CONCEPT]
Mercedes driver Lewis Hamilton said he was mystified by his lack of pace in the Russian Grand Prix.