Garry Monk's men may not have won since beating Cardiff 3-0 on February 8, but there were plenty of positives to take from Tuesday night's efforts at the Emirates Stadium.
The visitors' endeavour was rewarded when, with just seconds of normal time remaining, Leon Britton pushed into the Arsenal penalty area and stabbed the ball goalwards, which was partially blocked by Per Mertesacker, only to ricochet off goalkeeper Wojciech Szczesny and back onto Mathieu Flamini before rolling into the net.
Taylor believes the result - which could have been even better had referee Lee Probert not elected to blow up at the end of four minutes of stoppage time when Jonathan de Guzman looked to be breaking clear on goal - will stand the Swans in good stead for the challenges ahead, which continues with the visit of fellow survival battlers Norwich on Saturday.
"It just shows us we have got a bit of character and a bit of fight, and now we have got an extra point on the board which is encouraging," said Taylor, whose deep left-wing cross was powered past Szczesny by Bony.
"We are playing in the Premier League, so every game is pressure.
"There are so many clubs that are picking up points here and there and it is not over by a long shot.
"I think both ends of the table will go right to the end of the end."
Taylor added: "This league is like that. Weeks can go past and you think 'God, we have missed two or three games there where we haven't picked up anything', which is annoying.
"However, this does not change anything for us about Saturday now because it is still a must-win game.
"It is about digging in and making sure we stay in this league because we are in and amongst it (the survival battle) now and we have to make sure we do the job."
Head coach Monk is confident his men - now five points above the drop zone - can steer away from trouble if they continue to believe in their game plan.
"I know I will be judged on results, but we have been performing, yet without getting what we deserved," he said.
"A few times we have been sat in the changing room deflated, having not come away with anything, so the draw at Arsenal was vital and it is about momentum now.
"We started to build things again against Everton after being very disappointing against West Brom. The performance was a lot better and this against Arsenal has cemented it.
"Hopefully we can take it into Norwich and hopefully put on another performance like that."
- Sports & Recreation
- Wilfried Bony
- Wojciech Szczesny