It meant that the match had to go to a fourth set, which eventually ended up with a tiebreak being played.
Daniell and Koolhof had their noses in front through most of it, but the 39-year-old Bopanna ripped a winner, returning Daniell's serve on the first match point.
On the second Daniell put Cuevas's serve into the net, but with the third Daniell hit a volley at the net into open space for the victory.
In the second round Daniell and Koolhof will play Auckland raised Brit Cameron Norrie and Spain's Jaume Munar.
Loss for Routliffe
Erin Routliffe and Madison Brengle lost their first round match in the ladies doubles at Wimbledon 4-6 7-5 6-1 to Oksana Kalashinkova and Xinyun Han despite having four match points in the second set.
The New Zealand and American team, who were fortunate to make it into the Championships, will be kicking themselves at how they let this one slip away, with Routliffe serving at 5-4 and 40-15 in the second set.
Unfortunately though, that match winning point never came and the third set was a one-sided contest.
While this will be a tough loss to take, even getting on court was a bonus for Routliffe as she came to Wimbledon not really expecting to play.
She knew the combined ranking of herself and Brengle wasn't high enough to get them into the ladies doubles.
But as she had a friend to stay with in London, decided to make the trip over, rather than play an ITF tournament in Portugal.
As Routliffe will pick up $11,180 of prize money, it worked out to be the right choice, even though she came so close to earning more prize money.
It was an odd first set, with Routliffe and Brengle winning the first four games. But then the momentum went the way of their opponents, who themselves went on a three-game winning streak, before Brengle was able to hold serve.
The rest of games went with serve, so the New Zealand/American team went a set up after 35 minutes.
Han and Kalashnikova started getting into arguments as the second set went against them and at the change of ends they'd criticise each other.
The set got to a point where Routliffe was serving for the match. On the first match point she double faulted, on the second Han hit a winner down the line, with the third Routliffe went too long on a smash. The fourth, there was another winner from Han and Routliffe was eventually broken.
Frustratingly for the Brengle and Routliffe supporters, the set eventually went the way of Han and Kalashnikova.
Han and Kalashnikova won the first two games of the next set and momentum never went back to Brengle and Routliffe.
"Maddy and I are good friends and we were so happy to be in the draw," said afterwards, with her emotions still raw from such a painful loss.
"I had played Han before in Washington, with Alexa, so I knew her a bit, but I didn't know the other one as much, but Maddy had played against her a couple of times in doubles.
"We knew we had to be aggressive and play our games. Maddy plays very different to me, we're total opposites, so it did work.
"I think I let the moment get the better of me. Obviously I was happy to be in the draw, because I didn't think I was going to be, but then you start thinking during the matches.
"I just let it get to me a bit and then they started hitting a lot more of their shots and taking more control and we were on the back foot from 5-5 in the second."
