Coach Vern Cotter said they could go home from Melbourne for four challenging games against New Zealand teams.
The Rebels reminded them that they still needed to improve and had things to work on.
"We didn't start well, but managed to pull the game back and have better intentions."
The Blues faced a good arm wrestle during the first half and were going backwards.
"We were in trouble and probably lucky to be in front at halftime."
A yellow card conceded by first five-eighths Harry Plummer was a critical moment.
If they'd scored then, perhaps we would have found ourselves under pressure, and there may have been only six points in it, which would have led to a pretty exciting finish.
"Our guys got through the yellow card, did well during that period and then had a bit more in the tank at the end of the game."
Corey Evans did a good job at first five-eighths during that stage and Cotter was pleased with how the side adapted and responded to the extra pressure.
Cotter was impressed that despite the Rebels having 11 entries into the Blues' 22m area and the amount of possession they had, they could score only one try.
"We leaked a lot of penalties in that area, and preferably we wouldn't want to be in that position."
However, the win came at the cost of a head injury to centre Rieko Ioane, who will need to go through HIA protocols before he can play again, and he won't play against the Hurricanes.
Cotter paid tribute to the Rebels.
"They came away from Christchurch last week [0-39] and had a few things they wanted to show us on the paddock. Physically they were present but at the end they probably ran out of juice and we were able to finish on top."
The short turnaround from their injury-time win over the Reds meant they only had one full training session, which was not ideal preparation.