Bocanegra handed Rangers the lead 10 minutes into the second half and, after a goal from Inverness' Andrew Shinnie in the 67th, Lafferty scored his sixth of the season in the 83rd to rescue all three points.
Rangers won for the 15th time this season against just one loss and three ties and leads second-place Celtic, which visits St. Johnstone on Sunday, by seven points in the standings after its third straight win.
Inverness lost for the fourth time in its last five matches, and sits just one point off the bottom of the standings.
Bocanegra, a U.S. international, scored his second goal since joining Rangers last summer with a left-footed shot from 6 yards in the 55th.
Shinnie tied the fixture with a finish to the upper-right corner just over 10 minutes later, but Lafferty directed a right-footed shot into the net from the right side of the area from 12 yards to hand Rangers the win.
Rangers has seven wins and three draws at home this season.
Aberdeen 1, Hibernian 0
Aberdeen, Scotland - Scott Vernon converted a penalty kick in the 59th minute, and 10-man Aberdeen won its second straight to extend its undefeated streak to three games with a 1-0 win over Hibernian on Saturday at Pittodrie Stadium.
Aberdeen had just two wins through its first 16 Scottish Premier League games, but followed Tuesday's 2-1 win over St. Johnstone with another narrow win over Hibs to move six points off the bottom.
Peter Pawlett was sent off after 66 minutes, but Aberdeen held on for the slim victory.
Hibernian is winless in six, including losses in four of its last five, and is level on 14 points with last-place Dunfermline, but off the bottom on goal differential.
Hearts 4, Dunfermline 0
Edinburgh, Scotland - Stephen Elliott scored inside 2 minutes to spark Hearts to a 4-0 win over last-place Dunfermline on Saturday at Tynecastle Stadium in the Scottish Premier League.
Mehdi Taouil, David Templeton and Rudi Skacel also scored for Hearts, which had lost three of its last four games. Hearts, which is fifth, closed the gap on fourth-place St. Johnstone, which hosts Celtic on Sunday, to one point.
Dunfermline, in its first season in the SPL, lost for the fourth time during a five-match winless streak and is bottom of the standings on goal differential, as it trails Hibernian by seven in that category.
Kilmarnock 1, Dundee United 1
Kilmarnock, Scotland - Paul Dixon scored in stoppage time as Dundee United was able to steal a point at Rugby Park with a 1-1 draw against Kilmarnock in the Scottish Premier League on Saturday.
James Dayton put Killie in front after 51 minutes, as the club looked for its third straight win. But Dixon drove a 20-yard shot into the bottom right after 1 minute of stoppage time to split the points.
Kilmarnock, which is unbeaten in four, is sixth in the standings on 23 points. Dundee has two wins and two draws in its last five, and sits in seventh place on 22 points.
Motherwell 1, St. Mirren 1
Motherwell, Scotland - Jim Goodwin scored in the 59th minute as St. Mirren was able to earn a point at Fir Park on Saturday with a 1-1 tie against Motherwell in the Scottish Premier League.
Michael Higdon scored his seventh goal of the season early in the second half for Motherwell, which still extended its unbeaten streak to four matches as it picked up one point on idle Celtic for second place.
Motherwell is third with 34 points, seven behind Celtic. St. Mirren sits on 22 points from 19 games, and is eighth in the table.