Arsene Wenger praised the mental strength of his forwards after Arsenal saw off QPR to make the ideal start to a demanding schedule of five matches in 17 days.
A 2-1 victory at Loftus Road on Wednesday left Arsenal's manager relieved, with his side's position in the Premier League's top four cemented before they focus on overturning a 3-1 deficit in Monaco in two weeks' time in the Champions League last 16 second leg.
Olivier Giroud missed chances in Arsenal's home defeat to Monaco which would have given the tie a different complexion at its halfway stage had he taken them.
And Alexis Sanchez had been on a run of seven matches without a goal, but both he and Giroud scored within five second-half minutes to clinch Arsenal's seventh victory in eight matches, as they maintained their push to qualify for Europe's elite club competition for an 18th consecutive season.
If they are do so, Giroud and Sanchez will have to fire and Wenger believes this was evidence that they are capable of coming through testing times, in light of recent criticism.
"We were all down after the Monaco game and we responded well against Everton and again today. I think the confidence that we got against Everton paid today," Wenger said.
"He's strong mentally, Olivier. He can take some criticism and he's shown that but I feel it was a bit harsh for him. OK, he missed some chances but that can happen."
Arsenal had barely threatened Rangers' goal before Giroud pounced on Kieran Gibbs' deflected cross to notch up his eighth goal in his last 10 Premier League starts.
Arsenal could have been two goals clear moments later when Sanchez opted to pass when one-on-one with Robert Green, before a more selfless moment allowed him to beat the Rangers goalkeeper at his near post to end his barren run.
"It's good because when you don't score for seven or eight games it is on your mind even if you say it's not," Wenger added.
"But he took his chance well and he's tricky and has a short back-lift and scored a good goal. He never gives up and that's the strength of a good striker as well.
"He's resilient and I don't know what happened before. The fact that he still scored showed he has the mental strength to respond."
Rangers belied their lowly league position until Giroud made the breakthrough, with there being no discernible difference between the side battling for honours and the one fighting for survival.
Arsenal's class was ultimately enough to win the game, although Rangers gave them a fright when Charlie Austin fired in a superb effort from outside the penalty area with eight minutes remaining.
Rangers manager Chris Ramsey is a boyhood Arsenal fan but could find little satisfaction from his evening.
"I'm just sick for the players today, sick for the way that we've not got anything out of the game," he said.
"The players know that we are in the situation now because we haven't maximised our abilities, and they know that and are trying to address it.
"What happens is you end up where you are now because probably we've been relying too much on Charlie's goal efforts."
Reflecting on images of his friend and former Tottenham colleague Tim Sherwood rejoicing after a crucial win as manager of relegation rivals Aston Villa last night, Ramsey added: "There's nothing worse than seeing your rivals celebrating.
"Hopefully it will be us celebrating at the weekend, but we really can't focus on the other teams."