The Gunners were run close and Chelsea served a warning that the opposition are likely to be tougher to beat this term - although the poor pitch at Imperial Fields did not help either side.
Young defender Gilly Flaherty scored the winning goal 10 minutes before half time, poking home an Ellen White flick from a Kim Little corner, but the Blues had plenty of chances to score themselves.
Strikers Ashlee Hincks and Helen Lander both missed chances and Danni Buet also went close a number of times and Arsenal manager Harvey believes scorelines are likely to be closer this year.
"The occasion was great. We have been building up to get to this point for a long time," she said. "The crowd was good, the pre match stuff was good but performance-wise we are a little disappointed.
"The pitch wasn't great and that plays a part in how we want to play, which is to get the ball down, and we couldn't do that today which is a disappointing but we are just glad to get the three points.
"[Chelsea] were hard-working and organised - I think that across the league every team is going to be fit, organised and work really hard.
"It is going to be a slim one or two goal margin in every game - I can't see anyone getting beat four, five or six any more."
Gunners skipper Faye White shared her boss' views with regards to the spectacle, performance and pitch - and it is certainly going to require a lot of hard work from Arsenal to put their name into the history books by triumphing as the first Super League champions.
England captain White said: "It was a close game, both teams worked hard and Chelsea didn't make it easy for us and that is what this league has to be about - for people to think ‘what is the result going to be, which way is it going to go?'
"Do I think we can play better? Yes, certainly. The pitch was the same for both teams but it was very bobbly and hard for people to control the ball but we are going to have to learn to adapt to that."
With regards to the crowd - which was a record 2,510 - neither were surprised with the turnout but have stressed the importance of it not being a one-off and the need to keep attendances high.
"For the first game I thought there would be this many people. Now we have to try and keep that up for the whole of the summer and for each club that has to be the priority," Harvey added.
White agreed, saying: "I think it will gradually grow; in the summer when the men's clubs aren't playing it is a chance to come down to their women's club and get behind them.
"It is nice to play in front of a big crowd; you don't want to just be playing on your own. It is about young girls and boys coming and watching and, for the girls, inspiring them to want to be us one day - being role models for them."
– Pauline Courtois leads after first day
World Weightlifting Championships