Jackson Martinez and Juan Cuadrado both converted from the spot before the Inter midfielder netted a 30-yard screamer in the dying seconds
The Jordanians committed handball offences late in both halves at the Estadio Pedro Bidegain - the latter seeing a red card dished out to Anas Bani Yaseen - and the eighth-ranked Colombians made them pay via spot-kicks to James Rodriguez and Juan Cuadrado.
A raised arm from Rajaei Ayed Fadel in the 40th minute lead to Rodriguez's goal, before Yaseen grabbed a goal-bound ball with both hands to see red in the 83rd minute and Cuadrado converted.
A long-range effort from Guarin saw Colombia extend their lead in the 90th minute, with his powerful shot beating Jordan custodian Mohammad Shatnawi.
Colombia, as expected, took control of the contest early, but could not convert their dominance on the ball to goals as the Jordanians held firm in defence.
Mario Yepes' sixth-minute header from a corner was off target, but almost fell to Eder Balanta at the back post, only for the shot to have too much power.
Colombia front man Teofilo Gutierrez was looking dangerous at times when in space, but Jordan would create a chance when the ball fell to Ahmed Hayel after a cross in from Mohammad Al Dumeiri.
Al Dumeiri was fortunate not to concede a foul when he shoved Colombia's Camilo Zuniga out of the way on the left byline, but the referee waved play on - and the defender's cross in was flapped at by Colombia goalkeeper David Ospina, whose save fell to Ibrahim, but he could not convert from point-blank range.
Colombia failed to threaten from several set-pieces throughout the half, but got the chance to take the lead due to a brain-fade from Jordan's Fadel.
Fadel raised his right arm to brush the ball inside his own area in the 40th minute, and Rodriguez had no trouble converting the spot-kick two minutes later.
Defender Yaseen drew the ire of referee Pablo Diaz when he moved the ball on the spot - earning a yellow card for his troubles - before Rodriguez took his kick.
It was the third caution of the half, after tempers earlier flared on 19 minutes, seeing each of Yepes and Odai Al Saify go into the book.
Zuniga almost doubled Colombia's lead on 54 minutes, with his swerving strike from just inside the area coming back off the crossbar.
Colombia were continually frustrated by a lack of creativity up forward, although substitute Carlos Bacca should have had the ball in the back of the net for a second straight match - only his shot from the edge of the area was offline, and would not have counted after a foul for a high boot.
Jordan almost had the ball in the back of the net too - not that it would have counted due to offside - as Al Saify's headed into the left post from an Al Dumeiri cross.
Colombia almost had the sealing goal in the 80th minute, when Victor Ibarbo's cross found Adrian Ramos at the far post, only for the latter's flicked attempt on goal to find the side netting.
But moments later Pekerman's side sealed the victory from the spot again, as Cuadrado - another second-half substitute - coolly finished.
Guarin added polish to the scoreline in style, with a 30-yard rocket completing a 3-0 win.