The defenseman had a goal and an assist for the Rangers, who rallied to beat the Tampa Bay Lightning 2-1 and completed a sweep of their two-game, season-opening series in Europe.
"It feels good to chip in the goal," Redden said. "It's going to be my intention to keep building throughout the season."
Redden, who signed a six-year, $39 million free-agent deal with the Rangers during the summer, tied it with a power-play goal 3:47 into the second period when he blasted a shot past goalie Olaf Kolzig off a pass from Markus Naslund.
"Wade is a very calculated player, he's a very poised player," Rangers coach Tom Renney said. "He's got a lot of patience. He can process things quickly and yet make it look almost too calm. He did it tonight."
Redden said the long trip overseas, which included exhibition victories against Swiss team Bern and European champion Metallurg Magnitogorsk in Switzerland, was a total positive for the club that went 1-5 in preseason games against NHL teams in North America.
"We used the time well to get to know each other," he said. "It was good for everyone to get away and just focus on what we're going to do and what the team is all about."
The Lightning had only three shots on goal in the opening period, but went up 1-0 when Adam Hall scored after Rangers goalie Henrik Lundqvist partially blocked Andrej Meszaros' drive with 1:43 remaining.
Scott Gomez scored into an empty net 12:12 into the second period after Rangers winger Aaron Voros deflected a shot by Redden. Lightning center Steven Stamkos, the No. 1 pick in this year's draft, hit the crossbar late in the period and both teams missed a number of scoring chances.
"We've got to pick up some things," Gomez said. "We get so many shots and we want to put more goals in. But the bottom line is we took four points and we'll keep it that way."
Kolzig made 37 saves, and Lundqvist stopped 18 shots.
Tampa Bay coach Barry Melrose, in his first two games behind the Lightning bench is already frustrated.
"We don't compete," he said of the Lightning, who tied Los Angeles with an NHL-low 71 points last season. "We're too easy to play against. Until that changes we're going to have trouble. We have a lot of skill on our team, but skill means nothing if you don't work hard."
Melrose said he was disappointed with his star players, including captain Vincent Lecavalier, who just returned from a major shoulder injury. He heaped praise on the line centered by Chris Gratton that includes veteran wingers Hall and gritty, 42-year-old Gary Roberts.
"The best line tonight was again Gratton's line," Melrose said. "My biggest problem was I can't play Gratton's line every shift. It's probably the lowest-paid line we've got on the ice but by far the best line in the last two games.
"I hope our guys are embarrassed. We've just got to get our great players playing as hard as our lesser players and we'll be fine."
The Rangers also won 2-1 on Saturday in the season opener and return home with four points already in the bank. This marked the second successive year the NHL began the season in Europe, building off games in 2007 between Los Angeles and Anaheim in London.
The Pittsburgh Penguins played the Ottawa Senators in Stockholm, Sweden, later Sunday in another regular-season series the NHL hopes will increase the league's European presence.
As they did on Saturday, the Rangers widely outshot the Lightning.
The veteran Kolzig, playing his first NHL game with a different team after spending his first 16 seasons with the Washington Capitals, got the start in place of Mike Smith, who was in goal Saturday.
Kolzig made 23 saves before Redden finally got a puck past him.
New York held a 41-21 shots advantage in the opener Saturday.
Fans packed the 17,000-seat O2 Arena for the second successive day to see the first NHL games in the Czech Republic, even though the cheapest tickets were 20 times more expensive than the same ticket for a Czech league game.
"The audience? Outstanding!" Renney said.
The Rangers raised their sticks at center ice in their traditional victory salute to the fans.
"Because they're great fans," Renney said. "It's a great hockey city, it's a great hockey country, and we want to acknowledge the fact that we very much appreciate the support for both teams."
Forward Ryan Malone of the Lightning and Voros drew big cheers midway through the first period during their brief fight.
The crowd missed Jaromir Jagr, the former Rangers captain who left New York as a free agent and signed with Avangard Omsk of the KHL in Russia. The Rangers, however, had Czech natives Petr Prucha and Michal Rozsival in the lineup, while Tampa Bay countered with Vaclav Prospal and Radim Vrbata, who failed to impress.
"It was an unbelievable experience for me to play here," Prospal said. "It's just a pity I didn't score or have at least an assist. One goal is not enough to win."
It was the fifth time the NHL began its season outside of North America, with the other three times in Japan in 1997, 1998 and 2000. Renney and Melrose expect the league to return to Europe again.
"We're ambassadors for the game," Renney said. "Our legacy is to leave behind good things, and I hope we do that. I have no problem to come back to do this again."
"I think that any NHL team would love to come over," Melrose said. "I'm sure that the NHL will continue to do it every year. We've got so many European players, the fans over here deserve to see their homeboys play."
The Rangers will play host to the Chicago Blackhawks on Friday night in their first game back, and the Lightning will welcome the Carolina Hurricanes to Tampa on Saturday.