Boyd put the home team ahead before most of the crowd had settled in their seats with a goal after 34 seconds, but it was only when Cuellar made it two just after the hour mark that Rangers could finally relax.
Thistle caused occasional panic to the home defence with Cuellar clearing off the line and David Weir just managing to keep the ball out after his header had gone over his keeper's head.
Rangers took an early lead when Nacho Novo's superb pass put Boyd clear and from 20 yards the striker made no mistake with a powerful left-foot shot.
The visitors were rocked and DaMarcus Beasley had the ball in the net from a Barry Ferguson pass only to be adjudged narrowly offside.
Gradually Thistle came more into the match and Graham Bayne's lob drifted wide after the striker had beaten keeper Allan McGregor to a long ball from Russell Duncan.
Sasa Papac did well to block Bayne in the penalty area before Ian Black's volley was parried away by McGregor.
The home fans were becoming restless as Rangers struggled to break down a well-marshalled Thistle defence.
After the break Novo cut along the byline but Boyd headed wide. Weir then nearly conceded an own goal but managed to hook the ball clear after his header went past McGregor.
Rangers sparked into life after a double substitution with Jean-Claude Darcheville and Daniel Cousin coming on for Boyd and Novo.
Alan Hutton's cross was headed back across goal by Darcheville and from an acute angle Cuellar headed home.
Cuellar then performed heroics at the other end as he cleared off the line after Bayne's header had beaten McGregor.
Darcheville hit the side-netting from a Hutton pass before going even closer. The striker's clever ball released Hutton down the right and from his cross a Darcheville header crashed back off the crossbar.
Cousin and Darcheville saw shots blocked before the end but these three points keep Rangers in touch with Celtic and set them up for their Champions League visit to Barcelona in midweek.