Only two points now separate the top three, although Chelsea have played a game less.
Indeed, Sir Alex Ferguson suggested Arsenal "might yet mount the biggest challenge" after his Manchester United side leapfrogged the Blues with victory over Fulham.
Next up for Arsene Wenger's men are relegation battlers West Ham, while Wolves and Wigan also visit the Emirates Stadium next month.
However, there is also the small matter of a clash against top-four hopefuls Manchester City and the north-London derby with Tottenham at While Hart Lane to negotiate.
Campbell - the 35-year-old former Gunners skipper, who rejoined them on a short-term deal during January - maintains there is no such thing as a soft touch in the Premier League.
"We kept fighting and got the win in the end, and we do not care as long as the win comes," Campbell told Arsenal TV Online.
"It is never easy, you have to win and earn your rights, you have to play good football - nobody is just going to give you three points in this league, no chance.
"We just have to keep focused, picking up the wins and stay in there."
Arsenal's title credentials have already been written off more than once this season, most notably following successive defeats by their direct rivals at the start of February.
Therefore, Wenger is unlikely to give too much credence to the same critics now championing his side.
Denmark striker Bendtner remains happy to let other people talk while the Gunners go about their business.
"A lot of things are said in football, a lot of comments made - everyone has their opinions," Bendtner said.
"I cannot really say what is the difference [in Arsenal this season], but we are winning and just have to keep doing that."
The 22-year-old put his own inconsistencies behind him with another crucial strike to add to the hat-trick which sunk Porto and booked Arsenal's place in the quarter-finals of the Champions League.
Bendtner was glad to be back among the goals again, but stressed results, rather than individual performances, were the priority.
"I am happy to be scoring again after last weekend, when everything went wrong," said the Dane, who missed a string of chances in the 3-1 victory over Burnley.
"I was in all the right places but just did not finish. Sometimes this happens in football.
"Luckily, the chances which have come since, I have finished."
Bendtner told BBC Sport: "But the three points was the most important thing, whomever would have scored.
"Now we need to win the rest of our games so we can reach our targets."
Wenger is delighted his young squad have shown the strength of character to haul themselves back into the hunt following a fifth straight league win.
"With eight games - four at home, four away - left, we are still in the race, So let's have a go," the Arsenal manager declared.
"The rest of the season will be tight, interesting and exciting."
Arsenals' hard-fought win at the KC Stadium, where Hull produced a resilient effort following the dismissal of captain George Boateng at the end of the first half, was completed without the services of injured skipper Cesc Fabregas.
Wenger revealed the influential Spain midfielder could be back in contention for the visit of struggling West Ham as he nurses a hamstring problem.
Czech winger Tomas Rosicky also failed to make the trip to Hull because of a groin problem, but should be fit by the weekend.
However, centre-back William Gallas remains sidelined with a niggling calf injury, so Campbell is in line for another run-out against the Hammers.
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