O'Connor found the top corner with a free-kick from 20 yards on the half-hour mark and Hibs looked like repelling Motherwell's second-half pressure at Easter Road on Sunday.
But Law volleyed home from similar range with 10 minutes left of the Scottish Premier League encounter and Motherwell survived a late scare after Jonathan Page was sent off in injury-time.
Results at each end of the table had gone both teams' way on Saturday to leave a point welcomed by both sets of fans.
Hibs are now seven points above bottom club Dunfermline while Motherwell end the weekend as they started it, five points clear in the race for a Champions League qualifying place.
Motherwell manager Stuart McCall would have been especially pleased after his team came from behind after failing to trouble Graham Stack in the first half.
He was also without two key players through suspension and Motherwell missed the midfield control normally provided by Steve Jennings and the experience of Stevie Hammell at left-back.
Stuart Carswell came into midfield while Page started at centre-back with Tim Clancy moving out wide.
Clancy got the first effort on target when his powerful header was caught by Stack after Law's corner.
Hibs soon came into the game, with O'Connor and Leigh Griffiths linking up well but unable to carve a shooting chance.
Law hit a snap shot wide and Page was booked for a high foot on Stack as he tried to latch on to Michael Higdon's header.
Shaun Hutchinson produced a great block to stop O'Connor converting Tom Soares' cutback and Motherwell goalkeeper Darren Randolph appeared to touch wide Ivan Sproule's effort, although a goal kick was awarded.
O'Connor lit up the contest after Keith Lasley fouled Sproule as the winger ran at him just outside the box.
The striker fired a powerful effort round the wall and out of the reach of Randolph, who appeared to be unsighted by Clancy's attempts to block.
The Motherwell goalkeeper made saves from Griffiths and O'Connor as Hibs broke and Motherwell's only chance to level before half-time ended with Higdon unable to direct Chris Humphrey's cutback on target.
Soares went close to doubling the lead almost out of nothing in the 48th minute when he curled a shot against the bar from 30 yards.
Higdon soon had a great chance when Humphrey's cross found him six yards out following a short corner but the striker headed over.
Lasley and Hutchinson had shots blocked as Motherwell pushed forward but they were lacking a spark up front and Jamie Murphy replaced Henrik Ojamaa midway through the half.
Hibs left-back Pa Kujabi brought a comic element to the game with an atrocious free-kick, completely mis-hitting from 40 yards after taking a long run-up. Even the Hibs fans laughed before applauding him, presumably for his sheer audacity.
They might not have been so forgiving in different circumstances but their team were looking comfortable and Randolph had to stretch to save O'Connor's powerful strike.
But Motherwell were level with 10 minutes when Law fired home.
Substitute Omar Daley collected Hateley's pass inside the box and laid it off to Lasley whose clipped cross was headed out by Soares only as far as the unmarked Law.
The midfielder brought the ball down and his powerful volley left Stack motionless and nestled in the corner of the net.
Motherwell pressed for a winner but they were exposed in injury-time when Hutchinson lost possession on the edge of the Hibs box and Page brought down Hibs sub Roy O'Donovan as the pair chased the resulting long ball.
Page was shown a second yellow card and O'Connor had the chance to repeat his opener, only to shoot well over.
Motherwell brought on Steven Saunders for his first appearance since rupturing his Achilles in August but he had no time to make a touch as the game ended level.