Rangers captain Barry Ferguson tucked in the winning goal after the home side were given a scare by battling Falkirk.
Boyd opened the scoring at Ibrox
Kris Boyd put Rangers in front when he stroked the ball home from 12 yards but Bairns striker Carl Finnigan drilled in a fine equaliser after the break.
Ferguson applied a close-range finish when the visitors failed to clear a free-kick from Charlie Adam.
Falkirk pushed hard for another goal but their hopes vanished when Thomas Scobbie was shown a late red card.
Rangers manager Walter Smith made two changes from the side that lost to Hapoel Tel Aviv in midweek.
Libor Sionko and Adam were both drafted into the starting line-up, with Chris Burke and Gavin Rae on the bench.
Dado Prso, who was out of action for a month with a hamstring injury, was also named as a substitute and appeared late in the game.
Alan Gow started for the visitors as usual, despite signing a pre-contract agreement with Rangers last month.
A good save from Falkirk goalkeeper Kasper Schmeichel prevented the home side from taking an early lead.
A grounded Nacho Novo failed to connect properly with his pass to Boyd in front of goal and it rolled into the path of Ferguson but Schmeichel rushed out quickly to block.
After a scrappy period of play, the breakthrough came when Rangers took the lead on 34 minutes.
Falkirk centre half Darren Barr misjudged the flight of Alan Hutton's cross and Boyd did well to bring the ball down with his heel and flick it past the advancing Schmeichel.
Ferguson then blazed a shot narrowly over the crossbar from the edge of the penalty box.
Early in the second half, Finnigan tried his luck with a shot but goalkeeper Allan McGregor managed to block with one hand before Hutton cleared the danger.
Ferguson then released Novo with a precise pass but the Spanish forward smashed his shot into the side-netting.
Falkirk were on level terms after 64 minutes when Finnigan played a neat one-two with Gow and drilled a shot beyond McGregor from the edge of the penalty area.
But Rangers were not behind for long and it was skipper Ferguson who claimed the goal after an almighty scramble.
Adam's low, bouncing free-kick across goal was flapped at by Schmeichel and Sasa Papac's shot was blocked on the goal-line before Ferguson tucked the ball away from a tight angle.
Falkirk pushed on again and Finnigan headed a good chance over before McGregor made a fine save to keep out a shot from Stephen O'Donnell.
With eight minutes remaining, the visitors were reduced to 10 men when Scobbie caught Burke with a late tackle and was shown a straight red card.
Rangers claimed a welcome three points but there was a worry for the Ibrox team when Ferguson limped out of the action before the final whistle.
Rangers: McGregor, Hutton, Svensson (Papac 46), Weir, Murray, Sionko (Burke 66), Ferguson, Hemdani, Adam (Prso 75), Novo, Boyd. Subs Not Used: Robinson, Rae, McMillan, Furman.
Booked: Adam, Prso. Goals: Boyd 34, Ferguson 73.
Falkirk: Schmeichel, Uras, Barr, Holden, Cregg, O'Donnell (Craig 79), Moutinho, Latapy (Thomson 87), Scobbie, Gow, Finnigan. Subs Not Used: Lambers, Ross, Lima, Mcstay, Twaddle. Sent Off: Scobbie (82).
Booked: Holden, Finnigan, O'Donnell, Uras. Goal: Finnigan 64.
Ref: S Dougal