Last season's beaten finalists required a late winner from Robert Lewandowski to claim a 2-1 success at Emirates Stadium, but they more than held their own against an in-form Gunners outfit.
Henrikh Mkhitaryan edged the Bundesliga outfit in front, only to see Olivier Giroud level matters before half-time.
Lewandowski was to have the final say, as Dortmund struck on the counter, and Klopp believes his side are starting to recapture the form which saw them win a host of admirers in 2012/13.
He told Sky Sports: "It's a big step for us. Now we are back in the race, that's the most important message.
"I think most people thought it would be close, but the winner will be Arsenal. There were some moments in the game when it could be like this.
"We had one or two really close situations, lucky situations for us - when Mats (Hummels) was on the line and other things.
"But we were playing in London, it's a really hard game for us. But my team was very concentrated from the first moment, they did a better start in the game and made a better start in the second half. Then the match got more open, but that's normal.
"We didn't come here to dominate Arsenal in London, we came here to get a result - and that's what we did."