The visitors started proceedings with greater urgency, and were rewarded for their positive start when they opened the scoring in the tenth minute.
Rachel Yankey's raking cross field pass found Gemma Davison, who surged into the box before being recklessly hauled down by Sophie Ingle, leaving the referee with no choice but to point to the spot.
Kim Little stepped up and coolly despatched her penalty, sending the keeper the wrong way for her eleventh goal in nine games this season.
Chelsea had a chance to hit back almost immediately, but Dunia Susi, who was played through by Drew Spence, saw her low effort mopped up by Emma Byrne.
But Susi's blushes were spared moments later, when Dani Buet equalised in the most bizarre of fashions, curling her corner-kick beyond the flailing Byrne.
Chelsea's equaliser prompted a strong response from Arsenal, who began to attack with greater intent. Jordan Nobbs' snaking through-ball from deep expertly found Sophie Chapman, but the Arsenal skipper's low drive was smothered by Sarah Quantrill.
After soaking up wave after wave of Arsenal attack, Chelsea launched a rapid counter-attack, but Helen Bleazard, who was played through by Katie Longhurst, saw her tame effort easily saved by Byrne.
And against the run of play, Chelsea took the lead just two minutes before the interval. Susi, who had troubled the Arsenal backline with her movement and determination, was barged over in the box by Gilly Flaherty, and the referee awarded the second penalty of the evening.
Buet confidently thumped home from the spot to double her tally and send Chelsea in to the half-time break with an unlikely lead.
However, Buet nearly turned from hero to villain mere moments after the restart. The midfielder carelessly relinquished possession to Yankey, who strode forward and released Little, but the Scot's shot was turned behind by Quantrill.
From the resulting corner Jennifer Beattie was desperately unlucky not to level the scores when her thundering half-volley crashed off the crossbar and away to safety.
Chelsea were presented with the opportunity to put the game beyond reach, but Longhurst, who had latched onto a deflected pass, stabbed her effort against the post after finding herself one-on-one with Byrne.
And the hosts were left to rue their profligacy in the 72nd minute when Alex Scott's terrific lofted cross was met by substitute Kelly Smith (pictured), who looped her header beyond the reach of Quantrill.
Smith grabbed her second and restored Arsenal's lead in the 81st minute, nimbly swivelling inside the box and hooking her shot into the bottom right corner to cap off an impressive cameo.
And Little put the result beyond doubt with just six minutes remaining after she beat the offside trap and nonchalantly rounded Quantrill before slotting home her 12th goal of the season.
Arsenal boss Laura Harvey hailed some good fortune and her star substitute after watching her side secure a crucial win.
She said: "First half we were poor, second half we got a little bit better. We had a bit of good fortune at 2-1 when Kate Longhurst went through -- if she had scored, the game could've been away from us by then.
"I thought Kelly [Smith] did really well when she came on and her two goals changed the game."
Chelsea (4-4-2): Quantrill; Perry, Bonner, Williams, Ingle; Susi, Buet, Spence (Davies 90), Bleazard; Coombs (Lappin 79), Longhurst (Hincks 79). Subs not used: Telford, Lander, Rafferty. Bookings: White 45, Yankey 80. Red cards: none.
Arsenal (4-3-3): Byrne; Scott, Grant, Flaherty, Beattie; Chapman, Nobbs, Houghton (Smith 60); Yankey, Davison (White 81), Little. Subs not used: Harris, Tracy, Bragg. Bookings: none. Red cards: none. Att: 326 Ref: S. Rea