Lockwood fired Orient ahead from the penalty spot four minutes after the re-start then, with the home side coasting, Connor grab his fifth goal in his eleven starts since joining from Swansea.
The first half was a dismal scruffy affair spoilt by the wind and chances were few and far between but both sides did strike the woodwork.
After Orient's loan signing Wayne Corden saw a fierce shot block it was Boston who almost went ahead when defender Lee Canoville fired in a speculative effort from the right who rattled the Orient bar.
As the O's stepped up the pressure mid way through the half top scorer Gary Alexander, without a goal since January, sent one header wide of the mark and then rattled the post with another and his follow up effort was blocked by Paul Ellender.
After the break Orient quickly took a vice like grip and in four minutes were ahead when former O's defender Lockwood stepped up to blast his sixth league goal of the season past Michels Kuipers despairing dive. The goal gave orient a boost and they started to knock the ball around in style. Shane Tudor almost added a second being stretched with an ankle injury.
Orient, with six successive home clean sheets rarely looked like surrendering their advantage substitutes Donny Barnard and Joe Keith headed over before O's gave themselves a two goal cushion a from minute from time.
Following a patient build up on the left Keith sent in a cross, the visiting defence failed to clear and Connor from a tight angle fired into the corner of the net.