Gary Taylor-Fletcher fired home a cross from Keith Southern in the 77th minute to put Blackpool back in front but Rangers showed admirable spirit to hit back again when Connolly fired home a left-footed volley from 20 yards in the 84th minute.
The equaliser denied Ian Holloway victory against his old club but his men remain in the thick of the Coca-Cola Championship play-off race.
Holloway's reputation lay in tatters after he presided over Leicester's relegation to League One in May 2008.
Yet a year out of the game seems to have recharged his batteries and he so far proved an outstanding success since being appointed at Bloomfield Road in the summer.
Rangers - under Harford's guidance following the departure of Paul Hart earlier in the week - began brightly and Taarbat drove in a fierce shot from 25 yards which required a fine block from Adam.
Blackpool gradually assumed control of proceedings and in the sixth minute Barry Bannan engineered the space for a 20-yard shot which Rangers goalkeeper Carl Ikeme did well to hold.
The hosts' early pressure told in the ninth minute when Brett Ormerod crossed from the left flank and Adam arrived to drive a right-footed shot high into the net from six yards out.
The Scotland international is proving an astute capture following his £500,000 summer move from Rangers and this was his 10th goal of the season.
Rangers sought an immediate response but Taarabt flashed a shot wide from the edge of the 18-yard box.
But Blackpool generally held the upper hand as Taylor-Fletcher hit a shot wide from distance and Southern also went close.
Taarabt offered Rangers' most obvious goal threat but his luck was out again in the 34th minute when his close-range shot struck Blackpool defender Stephen Crainey and rebounded to safety.
Blackpool should have doubled their advantage before half-time when Bannan's dangerous outswinging corner from the left flank was headed wastefully wide by defender Ian Evatt.
Ormerod then fired narrowly wide shortly before the half-time whistle but Rangers drew level in controversial circumstances 10 minutes after the restart.
Referee Trevor Kettle provoked fury among the home supporters when he deemed Seasiders defender Neal Eardley had handled a shot from Taarbat.
Midfielder Taarbat - QPR's outstanding performer - stepped up to nonchalantly dispatch the resulting spot-kick and cancel out Adam's opener.
Hogan Ephraim then fired wide for QPR but Blackpool regained the lead with 13 minutes remaining when Taylor-Fletcher rifled home Southern's low right-wing cross.
Yet Rangers were not to be denied and were level in the 84th minute when Connolly hit a left-foot volley which flew into the top corner from 20 yards.