The Gunners maintained their slender one-point advantage over free-scoring Manchester City with a 2-0 win against Fulham at the Emirates Stadium through a brace of well-taken second-half goals from Spain international Santi Cazorla.
With almost no margin for error now, Wilshere accepts confidence will play a major factor in whether Arsene Wenger's squad can sustain what is a long-overdue assault on the championship.
"We must believe. If we don't have belief, we have no chance," Wilshere said.
"We take each game as it comes, but in the back of our head we are top of the league and we want to stay top of the league."
Wilshere accepts this season's championship battle looks set to be the most open of recent times.
"It is there for four or five teams to take, it is that tight, if anyone drops points it can change," the 22-year-old said.
"Manchester City are very strong at home and their away form has got a lot better as well. They will be one of our main rivals, but we have to play them here still.
"As long as we keep going, take it game by game we have a chance."
Arsenal took a while to break down what was stubborn resistance by Fulham at the Emirates Stadium.
Apart from an early half-chance through Mesut Ozil, when his scuffed shot was hacked clear as it rolled towards the corner of the goal, Arsenal created few real openings.
Indeed, but for a fine one-handed save from Wojciech Szczesny to palm away a dipping effort from Fulham midfielder Steve Sidwell, the hosts may have even fallen behind.
Wenger's team-talk worked, though, as the Gunners upped the tempo following the restart and pushed Fulham back to defend deeper and deeper.
Eventually the pressure told as, following a couple of goalmouth scrambles, Arsenal finally broke the deadlock when Wilshere's ball across the six-yard box was despatched into the bottom-right corner by Cazorla on 57 minutes.
The diminutive Spaniard soon swept home another just after the hour mark, this time sending a clearance from Brede Hangeland past Fulham goalkeeper Maarten Stekelenburg from the edge of the area.
Arsenal substitute Lukas Podolski could have added a third goal, but saw an angled shot blocked and then watched as Stekelenburg touched a bullet 20-yard shot onto the post.
Fulham forward Darren Bent had not been on long himself before being handed a sight of open goal when the ball bounced clear off Szczesny, but could not continue his good record against the Gunners as he stabbed wide from a tight angle.
Wenger feels his men deserve great credit for the high level displays they have produced.
"I am happy with the performance of my team because we have been remarkably consistent," said Wenger, who has played down suggestions a move was imminent for Juventus striker Mirko Vucinic.
"Let's not forget that we had a difficult start and we have shown all kind of ingredients technically, but as well mentally to respond to what happened to us at the start of the season. It was not easy."
Fulham will at least get some respite from their survival battle next week in the FA Cup fourth round at Sheffield United.
Cottagers captain Hangeland, recovered from a back problem which needed surgery, feels Rene Meulensteen's men can pull clear of trouble despite their lowly position just a point outside the relegation zone.
"It is real battle, but we are prepared to get enough points to stay in the league," the Norway centre-half said.
"We are playing a slightly different way now, we are very organised and all know what we are trying to do.
"It is about getting that transformed into results on the pitch, and I am confident that will happen."