Smith scored a late equaliser to send the game into extra-time, where goals from Danielle Carter, Shinobu Ohno and Casey Stoney proved enough for the 12-time winners.
The game proved topsy-turvy from the start, with Chelsea taking a 20th minute lead when Ji So-Yun converted an Eni Aluko pull-back.
Smith equalised for the Gunners two minutes later, heading a miscued shot from Carter past Marie Hourihan.
She denied Smith a second from the spot in the 36th minute, saving the England international's penalty after tripping Freda Ayisi inside the area.
Chances galore came and went after the break and it appeared Yuki Ogimi had won the game for Chelsea when she tapped the ball into the net after Siobhan Chamberlain spilled Aluko's effort.
But Smith wasn't finished and forced the extra 30 minutes with a sensational strike over Hourihan from 25 yards after having been denied from 30 yards by the crossbar.
She had a part in Arsenal taking a 3-2 lead, although this time it was her miscued shot diverted past Hourihan by Carter, who crossed for Ohno to make it 4-2.
Aluko gave Chelsea hope but Stoney thwarted them by heading home a corner to make it 5-3 and secure Arsenal's place in the final at Stadiummk in Milton Keynes.
There they will face Everton Ladies, who edged a spirited Notts County side 2-1 at the Impact Arena.
Two first-half goals from Nikita Parris proved the difference with County unable to find an equaliser in the latter stages after Katie Hoyle pulled a goal back in the 56th minute.