Saturday's 2-1 victory at Norwich left the Gunners with ten wins and one draw in their last 12 matches.
"We have some way to go to show that this is the right way," said manager Arsene Wenger, sounding a note of caution.
"Five weeks ago we were 17th in the league and I had to answer a question about whether I thought we would battle relegation.
"At the time I said no but in football things change quickly. We are back in a stronger position."
Next they play host to Bundesliga champions Borussia Dortmund in a Group F showdown at the Emirates Stadium, where they have not lost in 25 matches in the group stages of the competition.
Arsenal will be through to the last 16 for the 12th season running with a win, but they can expect a tough test against a Dortmund side who won 1-0 away to Bayern Munich in the Bundesliga at the weekend.
Mario Goetze scored the only goal in that game, and the 19-year-old will be the focus of much of the attention in North London, with Arsenal said to be keen to prise him away next summer.
The game comes in the middle of a massive week for Dortmund, who entertain Schalke in a local derby on Saturday, but Jurgen Klopp's side really need a win to keep alive their chances of advancing.
In the other game in Group F, Marseille entertain Olympiakos in the knowledge that a win could be enough to take them through depending on the result in London.
At Chelsea, the pressure on manager Andre Villas-Boas is increasing after they slumped to a third defeat in four Premier League games at the hands of Liverpool on Sunday.
The Blues travel to Germany to face Bayer Leverkusen in Group E knowing that a win will see them through to the knockout stages of a competition that owner Roman Abramovich is so desperate to win.
Their poor domestic form has led to suggestions that the Russian oligarch may once again look to appoint Guus Hiddink in a bid to rescue his side's season, but Villas-Boas insists he is not concerned about job safety for the moment.
"He didn't pay 15 million euros to get me out of Porto and another fortune to get me out of Chelsea," said the Portuguese in the wake of the Liverpool defeat.
"I have said we have set out to build something new at this club and the club is committed to what we are building for the future."
However, Abramovich's patience will be seriously tested if Chelsea slip up at the BayArena.
In what remains a very open group, Valencia are currently third on five points, but a win against Belgian outsiders Genk at the Mestalla will keep them firmly in contention ahead of their trip to Stamford Bridge next month.
Milan and Barcelona are already through from Group H, but meetings between the two clubs are always eagerly anticipated and Barca can clinch first place in the section with a win at the San Siro.
The Catalans, who travel without the injured Andres Iniesta and the suspended Dani Alves, are preparing to come up against Zlatan Ibrahimovic for the first time since he left them last year.
"It will be a very exciting, fantastic game," the Swede, who missed September's 2-2 draw between the teams at the Camp Nou, told UEFA.com.
"We will be playing against the best team in the world, without doubt.
"Even when I left the team, I knew I'd left the best team in the world. But, for me and all the other parties involved, I think the best solution was to leave the club.
"Given the results for both sides, it was the best solution."
In Group G, surprise package APOEL Nicosia of Cyprus can become the first Cypriot club to qualify for the Champions League knockout stages if they can beat Zenit St Petersburg in Russia.
Source: AFP
Source: AFP